Hi Arctic Wolf, I agree that is can be fun to separate people, it came make things look grim for them just before the end. The thing is though, I think they should all come back together at the final moment, to kick the bad guy together as a team. Maybe just the final round or so.
Maybe there is a tiny fourth stage. When they have been working together (yet seperate) to beat the guy, he realises that something is terribly wrong and he is losing. He then splits himself up between time. If even one of those fragments survives, he will be reborn in another time and/or is unkillable in the present.
So the last 50HP or so, he truly is a different enemy for each PC. Damage one does, does not effect the other. So the fighter beats his version of the bad guy. He now is sent back to real time. He can see that the guy is on his last legs and is dying. Thing is though, until all the shattered aspects of the guy have been slain, he is unkillable in this timeline.
So the fighter then has to hold the guy off, waiting for every PC to finish off their little bit of the guy. Then they all come back together in the main timeline and can finish him off. At this stage it is more of an execution.
Social interaction wise, I think this works as
A) Your PCs are cheering each other on
B) Each PC feels like the hero, as they "soloed" the guy
C) There is great tension, as how does the cleric do enough damage to the guy in time? Will the rest of the group live fighting the "present" for long enough for the cleric to chip away at his 'shard' of the guy?
D) In the end, only as a group can they succeed. It reinforces the teamwork.
Two suggestions would be:
1) Don't make the seperation stage last too long. Leaders and Controllers will really struggle during this period and Defenders are not doing their job, theives are not backstabbing etc. It takes everybody out of their comfort zone, which is only fun in moderation.
2) Have some way of the group using religion/arcana/nature to enter into the time-shard of somebody who is about to lose, or has lost. Otherwise the guy remains unkillable.
3) Alternatively, if any guy does lose his solo fight, then the party can use a skill challenge to cut off that segment of the BBEG, which makes him killable again, but will result in his surviving (much less powerful) in another time line. So he can come back one day.
Just some random thoughts to consider. Glad you liked the base idea.
P.S. Just had an idea for any character that does not have an epic destiny sorted out. In the end, they kill the guy, but he splits into 1000 pieces to be reborn at 1000 times over 1000 worlds. He gives a big muhahahaha. One or more of the PCs can then harness his energy, stealing part of his time portfolio. They then become his eternal bane. Everywhere he is reborn, they too are reborn and the BBEG is forced to play out defeat at their hands 1000+ times over until the end of time. A pretty cool ending for someone who has not got one sorted out, or who has the Eternal Champion, Demigod, Eternal Seeker, Wayfarer or a few other EDs.