Something I might like to try: Rather than have characters be married to their initiative rolls throughout combat, and rather than the hassle of rerolling each round, what about this? Allies can swap initiative counts from round to round. That is, the counts stay where they are, but you can choose a different slot from round to round.
One thing I like about this for PbP is that it lets things happen more organically, while to some extent preserving the round-by-round action economy D&D needs, and why yes I have been playing the Fantasy Flight Star Wars RPG recently, thank you.
So if the initiative roll looked like this:
1. Party (22, Oz)
2. Party (20, Shandrizar)
3. Party (20, Picayune)
4. Yugoloths (19)
5. Party (17, Graydon)
6. Party (13, Liliana)
7. The Jilted Planes (11)
8. Party (10, Shard)
9. Party (7, Rusty)
...then you'd have three party slots before the enemies, then two slots before the NPCs, then two more slots before the top of the round (or 5 slots in a row).
It opens up the floor to cinematic things where if you take the final slot of one round, you can also take the top slot of the next, allowing for extended, flashy combat sequences.
The main casualty here is spells which end at the end of your turn, or only last so many rounds. I'm not sure what the most balanced way to handle this is. Even though it's open to abuse, I'm inclined to say that the effect moves with you-- so yes, if you cast a spell that lasts until the end of your next turn at the top of first round and then hold your next turn until the end of the second round, then that spell does last longer. There's a level of metagaming tactics here, but I think I like that, too. And it can cut both ways.
...Another low-bookkeeping option is to just have an end-of-round curtain where all effects end. I've seen that work efficiently in some games, too.
If this all sounds too complicated, too meta, or too unbalanced to anyone, then no problem, we won't do it. This would be an experiment, and if you don't want to clutter up the game in that way, I completely understand. It's an idea that interests me, but I fully expect it won't appeal to everyone.