Usually I just open up pulls with Regen > Aero III > Thin Air > Holy x3, assuming the tank doesn't drop like a rock while I'm busy casting Aero III. I figured that's how you were supposed to do it because I see WHMs do it all the time in Expert.

After the stuns wear off I tend to get to where I'm alternating Cure II and Aero to try to keep my dots rolling. Thinking about it I had far less of an issue in Shisui of the Violet Tides(Except for that one Warrior who pulled the first two packs then swapped to his dps stance, that one I didn't manage to keep alive because I didn't notice he did that, so I was still trying to apply Aeros and he lost like half of his HP in an instant, and I couldn't get him back up, but I think that wasn't my fault so much), so I suppose once I get to Doma Castle Cure + Regen might be enough to continue dotting things.

One small note I've learned, Cure III's splash healing range doesn't seem to be very large. I remember on the last boss of Bardam's, I stood inside of the bird when everyone was still in the melee hitbox, cast Cure III on myself, and it hit no one. That suggests to me Cure III's not really useful outside of more organized raiding, unless I'm missing something.