I need to start getting smarter with healer CD use, I was mostly saving Thin Air for blade phase and some of the tighter Ukehis, using it during thunder tango sounds awesome.
A lot of it is just adjusting to the expectation that the other healer will explode into nothingness at any moment and having a plan B; AST has a lot of stupid stuff we can abuse pretty heavily to reduce some of the MP drain. Earthly Star is amazing as a top-off after Lightning spam pre-Ukehi--during the stun section planting it around the second party jump should let you pop it when everyone jumps back to the safe side after the last stun/lightning. and between that and a shield and Collective Unconscious it's usually a minimal MP-drain segment. Earthly Star is also a nice way to top everyone off at the end of the sword/orb phase without needing to waste a GCD on a direct cast, then pop off to the side, Collective, then Lucid + Celestial Oppo to extend MP regen time and keep the Celestial regen running on everyone a while longer. Pre-shield the tank buster, sit on Lady of Cups cards for bonus emergency oGCD heal, etc etc etc. Collective is also nice because everyone will instinctively run inside it a way they won't for Earthly Star/Sacred Soil/Asylum, which can make Cure 3'ing easier.
None of which is particularly helpful for you at all, I'm just rambling. Really the best thing that happened to me was probably having a SCH disconnect in the middle of P1 on an early learning pull and not make it back into the game for a long time. I got to figure out solo healing the sword thing and the first... three? I think? lightning sets in final phase before a bad bait over the safety line ruined everything, which was excellent preparation for figuring out cool down stuff without the fear of anyone blaming me if we wiped.
I've hit this weird cognitive dissonance spot where I still wish the fight was harder, but sticking with learning/clear parties to farm has been a really excellent way to get super familiar with the full extent of AST at 70. I still worry about what things are going to look like in PF in a month, but eh.