Gnome BODY (important!)

Talk it over with your players and figure out if they're actually onboard with this first.  The possible "twist value" isn't worth the possible "this isn't what I signed up for" factor.  And once you've had that conversation you're in a perfect place to transition into mining them for ideas which will be vastly better than anything we can give you since they'll come from the people you're playing with and who best know their own tastes. 

Talk it over with your players and figure out if they're actually onboard with this first.  The possible "twist value" isn't worth the possible "this isn't what I signed up for" factor.  And once you've had that conversation you're in a perfect place to transition into mining them for ideas which will be vastly better than anything we can give you since they'll come from the people you're playing with and who best know their own tastes. 

Burn down the too-big threats.  No unusable "can wipe 4-6 PCs with half his AP tied behind his back" Mary Sues like Destroyer.  No globe-spanning too-large-to-defeat organizations like VIPER.  Set the world up so the PCs have the opportunity to pick a thing they don't like and let the campaign be how they get rid of it.  Anything outside that scope has no business being in a superhero TTRPG setting. 
Do the same to the good guys.  Nobody wants to play a game where the GMPCs are just around the corner being better than the PCs.  Gut PRIMUS, UNTIL, all the other hero groups so the PCs can be important. 

I'd argue that the absurdity lies in permitting the device to drain Earth's defenses without explaining why it allows a 1 pip HKA to destroy the Earth in under a hundred Phases.  Of course an absurd assumption will create absurd results. 

Why not start with the game effects of these rings in the original game and translate them roughly into Hero System terms?

That has nothing to do with ranged Duplication.  All you need for that is non-ranged Duplication and Teleport that's either UOO or possessed by the duplicates.  ...And it doesn't even work, you run into the duplicate limit.  Your opponent just has to KO them all and keep them KO'd, then your Duplication is worthless.  You could patch that with the appropriate recombination modifiers, but those are explicitly allowed so I don't see what that has to do with ranged Duplication. 
 
But this is all moot, because you can do exactly as you describe with Summon and no other powers by just sitting back and summoning teleporters to attack your foe.  And yet there's no restriction on summons having Teleport.  Because at the end of the day, there's always a bullshit combination (Desolid overcome by SFX you know your foe lacks + an APW attack, for example) that needs a silver bullet to overcome and it's not worth trying to patch obviously exploitative holes that don't occur in actual play. 

Buy the appropriate Range Advantage.  See FREDp266 or 6e1p344. 

Duplication is all screwed up.  There aren't very many times you should use Duplication instead of just buying a Follower instead or using Summon.  It's expensive and has some real drawbacks to its use.  It's almost always better to use a different build.
 
Agent Smith probably just had a bunch of Followers (other Agent Smiths), or used Summon: Horde of Agent Smiths to fight Neo.  Trying to do it all with Duplication is a headache.

That has nothing to do with ranged Duplication.  All you need for that is non-ranged Duplication and Teleport that's either UOO or possessed by the duplicates.  ...And it doesn't even work, you run into the duplicate limit.  Your opponent just has to KO them all and keep them KO'd, then your Duplication is worthless.  You could patch that with the appropriate recombination modifiers, but those are explicitly allowed so I don't see what that has to do with ranged Duplication. 
 
But this is all moot, because you can do exactly as you describe with Summon and no other powers by just sitting back and summoning teleporters to attack your foe.  And yet there's no restriction on summons having Teleport.  Because at the end of the day, there's always a bullshit combination (Desolid overcome by SFX you know your foe lacks + an APW attack, for example) that needs a silver bullet to overcome and it's not worth trying to patch obviously exploitative holes that don't occur in actual play. 

That has nothing to do with ranged Duplication.  All you need for that is non-ranged Duplication and Teleport that's either UOO or possessed by the duplicates.  ...And it doesn't even work, you run into the duplicate limit.  Your opponent just has to KO them all and keep them KO'd, then your Duplication is worthless.  You could patch that with the appropriate recombination modifiers, but those are explicitly allowed so I don't see what that has to do with ranged Duplication. 
 
But this is all moot, because you can do exactly as you describe with Summon and no other powers by just sitting back and summoning teleporters to attack your foe.  And yet there's no restriction on summons having Teleport.  Because at the end of the day, there's always a bullshit combination (Desolid overcome by SFX you know your foe lacks + an APW attack, for example) that needs a silver bullet to overcome and it's not worth trying to patch obviously exploitative holes that don't occur in actual play. 

I would have reacted to his original question of how much of a limitation is appropriate to ask for but since he'd already gotten advice on that and he had already gotten a response from his GM, I didn't see a point in chiming in on that aspect of the conversation.
 
For clarity's sake, I was reacting to his statement of, "We won the fight, but the mentalist got away, so my character's power is growing/adapting itself to fight the last fight, in the grand tradition of militaries everywhere.  I do expect to encounter the mentalist again, likely soon."
 
It might be a grand tradition of militaries everywhere but it isn't a grand tradition in my Champions games. I deliberately try to not turn my Champions games into an arms race between players and the GM. I mean it's fine if the players and GM want to take a few baby steps down that slippery slope in their game. But I also don't see any problem with pointing out that it is a slippery slope. We're having conversations about the HERO system and its applications in actually playing games. And frankly, Panpiper was the one who brought up his motivations for asking the question so I don't see why you should be flummoxed if we politely discuss his motivations and whether we think it's a good idea for the GM to grant his request.  
 
 
Now I'll go out on a limb and get controversial
 
I understand the motivation: he didn't find the encounter to be fun so he's spending character points to try to keep the next gaming session against that opponent from not being fun as well.
 
But frankly as an outside observer, the game not being fun is something better addressed by a conversation between the player and the GM about how much he didn't find the session to be fun rather than spending character points to specifically protect himself from a future gaming session not being fun. 
 
If a GM sees a player feeling he has to spend character points in order to protect himself from having future gaming sessions not be fun, that should be a big red flag to the GM. A GM should use a villain very sparingly when having that one villain appear is irksome to the player(s).
 
If it were the GM asking the question of how to handle it, I'd recommend finishing out the story arc but have the villain primarily use his other powers and use hirelings of various sorts so various players aren't sitting there for 15-20 minutes at a time with nothing to do because the villain has a highly effective (remove player from the game) attack that he uses over and over.
 
A GM can always build a villain who is massively "unfair" or massively un-fun to play against. Or have the villains always behave in a massively un-fun manner (like the GM who has every villain turn every encounter into a hostage situation). A player shouldn't have to spend character point to counter the un-fun parts of the game...and the GM shouldn't make him feel obligated to do so.
 
 
Now to give some completely unsolicited advice:
 
I've had a couple of heroes built with "Hates mentalists" or "Hates enemy mentalists" which gives a convenient excuse for the character to work to develop mental defenses. That "drawback" also tends to give you an excuse to disobey of Mind Control commands easier and an excuse for targeting enemy mentalists first. If you don't like losing control of your character from time to time, I highly recommend that psych complication. It's also easier to work that into roleplaying than many other complications so enjoy it when you get the opportunity.
 
In general, if you get a second crack at some villain and you know it's going to happen, I'm a big fan preparing to kick the guy's butt. Have the team gadgeteer whip up something to flash the villain's targeting senses. Have everyone on your team target the enemy mentalist during the first phase, even if it isn't convenient. Use some detective work to track him down and ambush him when he isn't ready and isn't with his team. You don't have to play fair: the guy's a mentalist after all.

Sounds like she would be just as resistant to a Mind Control command to "Freeze in Place".  Which, I suppose, can easily be added to a Multipower with Mental Paralysis.  Toss on Unified Power and we're good to go. 
 
This just feels like a mechanic ("I don't want mental entangles to affect me") desperately seeking a justification.  But I'm also assessing it out of context.  In the right game it might fit right in.
 
My litmus test for "how big is the limitation" is "how often will it be relevant".  AT a -2, I would expect your EGO to be used for many other things (for which this extra EGO will be useless) at least as often as it is used to resist an entangle based on EGO.

The first three effects can be handled easily under Mind Control. Your breakout method can be switched to EGO/5 .
 
The slow is a Drain or Suppress vs SPD and Movement Powers
 
This is all fairly straight forward Hero. The only changes would be your recovery methods(an excellent approach to MMO simulation btw) and whether it would be an advantage or limitation.

My first thought is to pay 60 points for 12d6.  At an average roll of 42, I am guessing I will exceed Power Defense + BOD of virtually all targets, who now cannot attack ("Placate").  This leads me to think the base should be 10 points per d6, with "only attacks" or "only movement" being a -1 limitation.
 
I'm not sure this is superior to using the Entangle rules  to create an effect that prevents attacking or movement, a Mind Control construct, or even a Change Environment (e.g. target must make a X roll when attacking or select a target at random).

Burn down the too-big threats.  No unusable "can wipe 4-6 PCs with half his AP tied behind his back" Mary Sues like Destroyer.  No globe-spanning too-large-to-defeat organizations like VIPER.  Set the world up so the PCs have the opportunity to pick a thing they don't like and let the campaign be how they get rid of it.  Anything outside that scope has no business being in a superhero TTRPG setting. 
Do the same to the good guys.  Nobody wants to play a game where the GMPCs are just around the corner being better than the PCs.  Gut PRIMUS, UNTIL, all the other hero groups so the PCs can be important. 

You need to define "Stomping" first.  Right now you have SFX and need to turn that into mechanics. 
Does it require the target be prone, or can you stomp on somebody's toes while they're standing? 
Does it require you to stay standing on the target (a "foot based grab") or can you Stomp-By? 
What about targets smaller or larger than you, does that change anything? 
So on and so forth. 

You need to define "Stomping" first.  Right now you have SFX and need to turn that into mechanics. 
Does it require the target be prone, or can you stomp on somebody's toes while they're standing? 
Does it require you to stay standing on the target (a "foot based grab") or can you Stomp-By? 
What about targets smaller or larger than you, does that change anything? 
So on and so forth. 

This sounds to me like a conversation that should involve your group, not some random strangers on the internet. 
 
Tell them you are [enthusiastic/ambivalent/hesitant/concerned/whatever] about the idea but before moving forward to [saying no/saying yes] you want to have a dialog about [the questions and concerns you have, such as the ones you raised in your post] so you can be sure everyone's on the same page and onboard with the idea. 

Burn down the too-big threats.  No unusable "can wipe 4-6 PCs with half his AP tied behind his back" Mary Sues like Destroyer.  No globe-spanning too-large-to-defeat organizations like VIPER.  Set the world up so the PCs have the opportunity to pick a thing they don't like and let the campaign be how they get rid of it.  Anything outside that scope has no business being in a superhero TTRPG setting. 
Do the same to the good guys.  Nobody wants to play a game where the GMPCs are just around the corner being better than the PCs.  Gut PRIMUS, UNTIL, all the other hero groups so the PCs can be important. 

I do hate hearing the only minor inconvenience argument.  I am wearing a face blanket in mid July.  So, I am making constant save rolls vs passing out.
 
No offense, but it does make me wonder if people who are saying that are wearing their mask.,

Burn down the too-big threats.  No unusable "can wipe 4-6 PCs with half his AP tied behind his back" Mary Sues like Destroyer.  No globe-spanning too-large-to-defeat organizations like VIPER.  Set the world up so the PCs have the opportunity to pick a thing they don't like and let the campaign be how they get rid of it.  Anything outside that scope has no business being in a superhero TTRPG setting. 
Do the same to the good guys.  Nobody wants to play a game where the GMPCs are just around the corner being better than the PCs.  Gut PRIMUS, UNTIL, all the other hero groups so the PCs can be important. 

I'd say that the STR increase granted by the charge(s) does not cost END to use, but the base STR still costs END. So, if you have a 10 STR and a power that gives you +40 STR on continuing charges, you could use 50 STR where the +40 costs 0 END (because of the charges) and 2 (or 1 I don't remember) END for the base 10 STR.

I'm with you.  I regret giving it the one PC I made for another player. 
 
My big problem with it is that it's so variable.  I can't just say "Oh, Findo is going to have enemies at 1/2 DEF so he should be capped to 40 AP instead of 60 AP" and wash my hands of the matter. 
He might botch his first roll and be useless unless he has a 60 AP attack to fall back on.  He might slam out a success every round and be facing virtually zero DEF.  He might slam out a success every round but be targeting basic DEF when the opponent only had 6 base DEF and a truckload of Armor so the Find Weaknesses were wasted. 
If Find Weakness were just "Make roll, if successful target has 1/2 DEF against you" it'd be a lot easier to manage.  It's not. 
 
Though half my problem is that the player can't remember how Find Weakness works.  Or how to roll to-hit.  Or how to count BODY.  Or where on their sheet their CV is. 

Why not Naked AVAD (Half of target's [appropriate defense]) for [your AP here] of Attack Powers, Activation Roll [whatever number you want]-, Extra Time (Half Phase Action, only to Activate)? 
If you want Lack of Weakness too, add Activation Roll Subject to Lack of Weakness.
  
I agree.  I don't see what having a billion defenses achieves other than complexity and arms races. 

This is absurd.  Gandalf970 asked a very straight-forward question with a very straight-forward answer and nobody's managed to even touch on it. 
 
@Gandalf970 Reference FREDp296, FREDp297, 6E1p381
 
All that's needed to disrupt casting is to land an attack that's not totally negated by defenses.  A single point of STUN or other such effect is enough to cancel the entire spell. 
The procedure thus becomes holding one's action until the caster casts, winning the DEX vs DEX roll to act first when the caster casts, hitting, and dealing any damage.  This negates the spell, with nothing the caster can do at this point. 
 
6E's Fantasy Hero contains text on page 165 that indicates Gestures and Incantations begin at the start of the Segment, and thus holding until the caster's DEX and the DEX vs DEX roll are unnecessary, making the process even easier.  Just go first on that Segment and hit them.