I wonder...if you eliminated opportunity attacks for the most part except for those that involved marked creatures, would combat speed up?
Some, I suppose, but you would be enhancing the striker role (which is mobile), while devaluing the defender role (significantly, in the case of the fighter).
You wouldn't have to worry about whether or not you moved such that you'd get an OppAttack...
Do you usually find Opportunity Attacks taking the bulk of your game-time? In my experience, they influence tactics on the battlefield, but don't take that long to resolve (although, if your intent is a more fluid battle-field, this definitely should help).
...and it would reduce the amount of extra attacks (that usually don't do much damage).
Those extra attacks
can do a
lot of extra damage if your leader(s) are buffing defenders properly, especially at higher levels. And don't forget, every roll is one more chance to crit (which some characters are built around).
With all that in mind, if you really want to speed such attacks up, some, anyway, you could simply give out the average melee basic damage (like a minion) for each opportunity attack (this could be recorded on the character sheet. (Although, I reiterate, this devalues the crit-build character.)
You could streamline even further by making this auto-damage (although this
over-powers the fighter, who also
stops a creature on a successful opportunity attack.
Personally, I don't like either of those options. If I was going to eliminate/streamline opportunity attacks, I'd do it selectively:
Defenders, Soldiers, and
Maybe Brutes would still get to use them. No one else would. (This would negatively affect melee-leaders and melee-strikers, but they would benefit so much from most monsters lacking opportunity attacks that I think it would balance out.)