Average damage is an interesting idea and might work quite well. I'm trying to think of ways it might break the system and not coming up with much. As long as you adjust for things like Brutal, and nobody has any powers that grant damage re-rolls, you should be good; just mark each power with two numbers for damage, one for standard hits and one for crits.
The suggestion to try moving away from the battlemat might be a good one. My experience is that it drastically speeds up combat and punches up both energy level and immersion; but that experience is all pre-4E, and I'm not sure how well it translates.
Still, in theory it ought to work. Ditching the battlemat forces everyone to accept that combat positioning is going to be vague and imprecise, and therefore to stop sweating the small stuff. It also means players spend their combat time imagining the scene in their heads rather than counting off squares on the grid, which a lot of folks find more immersive and satisfying.
Another thing that could help is to overhaul everyone's character for playability. Obviously you don't want to dictate anybody's character choices, but if your players feel the same way you do, you can gently urge them to do the following in the name of speeding things up:
- Any number that can be pre-calculated should be.
- Avoid feats and at-will/encounter powers that grant situational or short-term bonuses, especially party-wide bonuses. Daily powers that grant bonuses are usually okay.
- Try to standardize your attacks so they all have the same to-hit bonus*. Pick powers with the same attack stat and weapons with the same proficiency bonus. If all your attacks are +14, you quickly get used to adding +14 to every attack roll, instead of having to look up a different number every time. Melee warriors with a non-Strength primary stat should consider picking up Melee Training.
- On your character sheet, write down the attack bonus, target defense, and damage dice (or average damage) for each of your powers. Something like this: "Cleave: +14 v AC/1d10+8." Put this information next to the power name in the list on the back of the main page. When you just need those numbers, it's much quicker to scan the back of your character sheet than it is to shuffle through power cards.
And some in-play tricks:
- As others have said, roll attack and damage simultaneously.
- For attacks with multiple targets, make all the attack rolls simultaneously. Grab one d20 for each target, then roll the fistful and target them "as they fall" - in other words, the die that lands farthest to the left is assigned to the target that's farthest to the left. This does require a certain amount of trust in your players to assign their dice honestly as they see them.
- Remember that burst and blast attacks use the same damage roll across the board. Roll damage once, not for each target.
- Consider imposing a time limit on how long people take to decide on their actions. If you don't announce your action within 10 seconds of your turn coming up, you don't act that turn. (If you're feeling generous, allow them to take their second wind instead.)
Finally: If combat is slow and frustrating for your group, you can simply cut back on combat! Focus on RP and skill challenges instead, and reserve combat for the big showdowns.
[SIZE=-2]*Characters with both weapon and implement powers may have to settle for having two attack bonuses, one for the weapon and one for the implement.[/SIZE]