MC, if you want to speed up combat - and I don't see why you wouldn't if you want the game to go well - here's what I do as a PBP DM:
- Asking players to roll initiative is a waste of time, as is waiting for the next guy (or gal) in the initiative order.
So what I do is that the DM rolls initiative for the PCs as a group, using their best init mod. When it's the PCs' turn to act, they act in order of posting - first post first served. The DM resolves whatever is needed (such as enemy mortality) after each post, if he gets to it before the others post. Then the NPCs act, and then the PCs, etc.
- I also prefer that the DM makes most rolls. If the player wants he can roll on IC; otherwise, the DM rolls.