Well we're actually moving off topic, but to the real topic (ie. your problem isn't which rules to use, its how to speed things up).
I can't help you with WebRPG or one of those apps , I haven't used them either. Obviously, there are products out there like those, GRIP, my chat scripts, special chat rooms, etc that can automate damage tracking and die rolling. On the other hand, how long does it take for me to say, "I swing with my sword. 16, for 12 damage if I hit" and then you respond with the actual result (checking the AC, etc). Not very long, so those tools only shave seconds off response time.
Playing mini-less is the way people had been playing D&D for years, so that's not a problem either (
www.montecook.com for a great DM article on playing without mini's).
Having a ranger wanting to swing on a vine while attacking's pretty hard to model without a human GM, so that's an area where only you can arbitrate. Thus the fancy openrpg programs will not entirely help in that regard. Even the cool NeverWinter Nights thing might need your help (or the Ranger simply wouldn't be able to do it).
I suspect, your biggest problem is simply having 6+ players. More players equals more delay between each player getting a turn. Hence the WoTC 4-player standard (which is really 4 PCs + 1 DM = 5 players). It's a actually a good rule of thumb for any game design. Most games bog down, when I have to wait for more than 4 other "actions" to be resolved before my turn.
Here's some ideas along those lines:
Run less combat, more RP: chat rooms are great for chatting, so run more encounters where there is more yap, and less hack.
Run fewer Players: take the 4 most reliable, best players and keep them, let the others go (best trick is to "split" the group into 2 games, whether you run both is up to you).
Read monte's mini-less article: after so much mini use, we forget how to run without them. Mini's define things for us quickly, but also constrain our game play in we only think to do what the movement rules let us. Here's a link:
http://www.montecook.com/arch_dmonly21.html
Check to make sure you've got the most optimal game tools available and learn to use them. You can speed up aspects of the combat, which will get you some gain. There are forums, and the like for using those tools, go hunt them down. Let me know if you want my mIRC scripts (in your MUCK, that might not be possible, but then a MUCK might have its own scripts). You'll have to hunt around and test with a friend.
Anybody else got some tips on speeding up combat?
Janx