Re: running combat with the speed chart
Our group typically uses either a spreadsheet on computer (the other GMs typically have a laptop in front of them when they run; I don't) or printed spreadsheet (me!) when we run combats. The GM will call out who's next to go rather than Segment/Dex. Now we're mostly Hero veterans, and those who aren't will say what they want to do if they want to go 'out of turn' and the GM translates it.
In convention games I encourage newcomers, so I try to make the rules as painless as possible. I keep the SPD/DEX chart and call out who goes when, while telling the players up front to just let me know what they want to do and I'll translate it to the rules. Also I tend to have most PCs at the same SPD, sometimes with a high and a low SPD in the mix, "Okay, Martial Arts Chick is really fast, but she doesn't hit so hard, while Strong Guy hits really hard but he's kinda slow...".
So in our group most of the responsibility for calling who goes next is on the GM rather than the players, but we're mostly veterans and if a GM mistake is made it ususally gets caught quickly, and in my own convention games I try to take as much of the responsibility as possible.
Works well for us.