Unless I've messed something up with stacks, I just leave Garuda-egi on the boss (or Straf Doll, we only kill one). I usually toss an Aerial Slash on my Jagd, but that's usually it.

In leg 3/4 I just feed the Jagds as soon as I can; I generally get one last tick of Bio II + Miasma as I'm feeding, so I leave a little buffer HP. I'd rather risk the damage be a little higher than desired than risk having a dead doll.

In final phase, I generally end up switching back to the boss for a few GCDs in the middle. I wait until the Jagd does its 3rd stacking AOE before feeding, so I don't need to be on it the entire time.