I think for Turn 1 with the DPS burn, it is an unplanned way to overcome the fight (instead of each group feeding slimes). For this, I think heavier heals will be required as the result of the risk.

And short of carrying a Mega Ether (may be enough MP between Shrouds), I cannot think of anything technique wise AND on the individual level that will let you have more MP during these parts of the fight.