Some general AST dungeoning tips from me though I am not an AST main by any stretch of the imagination...
Mainly heal in Dirnal. The thoroughput of a regen will beat the pants off of a shield every time. More HP per MP despite the Noct healing potency buff.
Swap to Noct between pulls/before a boss and toss a shield on the tank when you can. It will likely get eaten while he runs but better that than his health.
Use Collective Unconscious. It isn't just for the 10% mitigation the regen it applies is hefty. It's also a regen available to you in Noct stance if you insist on healing in Noct.
Speak up for yourself if you can, spend your MP wisely. If a dps is eating tons of AoE to a point where you're healing them like they're another tank let them die. You can raise them but maybe the death will get their attention since the flasy orange circles apparently didnt.
Use the direct heals (Benefic/Benefic II/Helios) more than the Aspected versions in general. Aspected Benefic specifically can be a huge MP sink.
In a situation with an AST and a WHM I am usually the WHM. WHM is better equipped to handle things like stack markers (with Cure III) and raidwide damage where as AST (in this situation) is the better choice for a tank healer. Keep Earthly Star active to heal through tankbusters when you can, between that and ED you should be able to baby the tank. You have to trust your WHM cohealer's regens as well though - plenty of time I heal through something like Diffractive Plasma in O7n with a Medica II and see an AST/SCH pop Aspected Helios/Succor after the damage comes out. Why? People aren't topped up but there also isn't more incoming damage so let Medica II tick and bring them up naturally.
If you still feel like your cohealer is dps-happy maybe say something? At the end of the day none of us are mind readers and Stone IV is a potency gain from Malefic III so the WHM's dps should be higher than yours.