After playtesting my game (COR), I realized that it's too slow. Way too slow for such a simple game. The issues that I think are trouble are:

Too many die rolls. Some characters may roll 16d20 in a turn of all-out attack(not to mention defense rolls if they are attacked). The initial reason was that I thought it would be more fun to roll more dice, but that doesn't seem to be so. There is also a lesser benefit for high-Accuracy characters versus high-Damage characters, because a high accuracy results only in a hit, whereas a high damage results in what could be a one-turn kill. I am reluctant to edit the dice mechanic, as it is deeply integrated into magic (most attack spells penalize die roll totals). So, my question is: How can I reduce the amount of dice rolled while maintaining the benefits of die roll total changes?

Also, there is the multiple-character dilemma. These rules aren't on the site, but a player can choose either one strong character or two weak characters at character creation. When the latter happens, the amount of dice rolled by that player doubles, and game-play gets much slower. Still, this is one of the more popular aspects of COR (among the few people who have played it), and it helps to keep a player excited about the game even if one of his characters cannot act (frozen, time-stopped, dead). So, the question here is: How can large-party groups stay moving quickly?

These are the main problems, but the start of battle also happens slowly, and new players are slow to decide what to do. If you want more info, e-mail me at cor@xasamail.com . Thanks for reading.

What, specifically, do you consider the benefits of die roll total changes?

Since you value them, I assume that you have some goal in mind that you have found (through experience) that they work well for. But you're probably going to have to get away from them. If I want to offer you something that will fit the same bill, I need to know what the bill is.

Rolling a bunch of dice isn't that bad, so long as you can do a couple at a time.

Do not make the dice totally dependant, maybe have a few sets of rolls that can be done at the same time.

Maybe roll other dice than just 20 siders

And, if you can roll all 16, without looking at a table, you'll notice it takes about 10 seconds, which isn't that bad. Its probably looking values up that slow things down rather than just the specific dice rolls.

Or take away a few dice and add a trade off system; Let them choose between a few options that have trade offs.

This may be very extreme, but rolling large numbers of dice is almost certain to give you average results. Put another way, the amount of randomness in the roll is very small. Put still another way, there is very little point to actually rolling the dice (as opposed to just using the expected value).

So...you could consider putting a (low) cap on the number of dice actually rolled. Anything above this cap, you use the average.

Example: say you set the cap at 5 dice, and the character has a pool of 20 dice. You would roll the 5 dice and take the average for the other 15, so your roll would become

5d20+15*10.5 = 5d20+157.5 =~= 5d20+158

The average to be added could be a simple table-lookup.

Of course, that does kill the joy of clattering 20 dodecahedrons on the table...
SR
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Ah, now we're getting to the meat of the game. In brief, I chose d20s because they average out to 10 (well, 10.5, but...) As this was chosen very, very early in design, several mechanics are built around this. First is the Speed Ability and the Bonus Move action. A Bonus Move gives a bonus to (here it comes) dice roll totals. The bonus uses a messy formula (I know, figure out some change): 3(3+SP). The (3+SP) is called mov, and a Bonus Move gives you a bonus, distributed as you choose, to any of the 4 Dice Roll Totals (Gah, I'm abbreviating it to DRTs). At 0 SP, you get a bonus of 9 that you can distribute (close enough to 10, plus distribution helps). So, the fact that a Bonus Move is an action and gives about 10 DRT additions makes one action worth about one character point (1 rank in an Accuracy score adds 10.5 and costs 1 char pt.).
So, now we know that an action is worth a char pt., but if the die type is changed, everything changes. Also, we can see a benefit of DRTs. Next up is Magic. The Magic system in COR (or at least the one in my hopefully-to-be-published product, LoserQuest) uses only two spells that add to Accuracy or Damage. Almost all of the other attack spells penalize a target's DRTs (Chill, Thorn, Disease, Acid, Flame, Sand, etc. all do things like vision impairment, numbing, weakening of the body, and so on.). If I change the way DRTs work, that means revamping almost every game I have made with COR.
I've talked about a lot of problems, but I may have a solution. I need to know whether this type of thing works, so if anyone has used this kind of system, your advice is invaluable. My idea is that instead of rolling an army of dice, you roll one die and multiply it by your ranks in an ability + 1. This makes things a little easier in one way, but people who are bad at math will have trouble. Maybe if there was a one-page table with all the rules needed...? This change greatly increases randomness, which I think could be a good thing (now high-defense characters have to watch their backs against low-Accuracy opponents). Well, what do you have to say, Forge-goers?

Can you utilize some other feature of the dice besides adding up the numbers? That's one way to stretch less dice out. Lots of things on the dice can be meaningful, like
How many came up even, how many came up odd?
How many 'of a kind' did you get?
Did you get a long string of sequential results (3,4,5,6,7...)?
Many of the highest or lowest possible roll did you get?
Do any of the digits exactly match some relevant attribute on your character sheet?
For example, a simple widget like "All even die results are doubled" will give you the same spread of possible results with 2/3rds the dice.