Time Limit allows an Instant Power to be available for a the specified Time Period, ready to be activated as a Zero-Phase Action (Attack Actions still apply to use them offensively) during the entire period. It's generally used when the Power can't already be activated as a Zero-Phase Action, which means it really isn't applicable to a vanilla Blast Power (or almost any base Power, as just about every Power in the book defaults to only needing a Zero Phase Action to Activate).
This does mean Continuing Charges with Clips & Reload time can be added to Powers with Time Limit.
But I don't see them interacting the way Lucius describes based on what each Modifier actually does. There's nothing that prevents Blast from being activated without prep at any point, aside from the 1 Hour Cool Down, which isn't perpetration so much as a waiting period.
Now; if you had Extra Time: 1 Hour plus Time Limit: 5 Minutes - THAT does what Lucius is trying to accomplish: there's a 1 Hour period the Power is not available and then a 5 Minute Period you can use it without the Extra Time aspect being required.
Of course, Extra Time runs into the same problem as the 1 Hour To Reload aspect - it assumes nothing else is being done except that Action. Which also isn't what is being asked for.
Breaking down why each of these builds isn't achieving the goal as desired based on what the Modifiers are actually doing:
Extra Time: can do nothing else during the initial activation period - not a waiting period
Time Limit: can activate a Power as a Zero-Phase Action for powers that already can't be activated as a Zero-Phase Action, during the Period specified - this almost does what you want, but doesn't include the cool down period; still it might be a viable option (assuming you want to take an Advantage for something that can already be done inherently)
Charges, Continuing + Reload;
--The Power lasts the duration, assumes it's basically a continuous power (which Time Limit is a pseudo-continuous Power in that it's available for specified length, but not always active); Continuous assumes the Power is actually Active for the entire period (addendum: using Fuel aspect means it turns on/off at will, and the Continuous Charge lasts the total time In Use, but not consecutively);
-- Reload runs into the same problem Extra Time does, assuming that's the only action being taken.
-- Also, the number of Charges limits how often the power can be used Period. 16 Charges means you only get 80 Minutes of Continuous Use per Day/Session. Which is actually less than you can fit into a 24 Day assuming basically 22 hours of waiting and 110 Minutes of use... (plus 10 minutes left over to maintain the weapon and complete a 24 hour cycle...)
-- Charges means the Power isn't using Endurance, not sure that's a feature or a bug in the desired end result. [I hate that Charges mess with Endurance]
None of these really interact as described/desired in my opinion.
What the system really needs is a full fledged out Cooldown Limitation with a "how long a power can be ready for use" and "how long between ready states" aspects;
Default being Ready For Use/Used for 1 Phase; Must Wait 1 Phase To Use Again (usable every other Phase for, I dunno, -1/4); and start stepping up and down the time charts. +1/4 for Use Time going up the chart (can be Activated any time for 1 Turn +1/4, 1 Minute +1/2, etc); and Must Wait 1 Turn -1/4, 1 Minute -1/2).
If a Power can be Activated and must wait 5 Minutes between uses that would math out to a -1 Power. (start at -1/4 Base, -3/4 for stepping down Cooldown from 1 Phase to 5 Minutes)
So, a Power can be used for 5 Minutes, and has a 1 Hour Cooldown: Base: -1/4; 5 Minutes Of Ready State (+3/4, total of +1/2 Advantage so far); Cooldown of 1 Hour (-1; total of -1/2 Limitation);
Eh, that's gonna be a weird Limitation, I'd have to sit down and play with it some to really determine what's a good way to build it out;
This post got long, so I'm going to end my thoughts here; only last point to make is that 5 Minutes of Use is effectively unlimited use for a single fight with no limitations; and this only becomes a limiting power for prolonged encounters and/or multiple encounters in a short period.