Use Sinastry.
Once double prey pops up, don't panic and throw one or even two heals to your tank, 6 seconds is a lot before prey starts happening. Then switch to your pray mark and unleash all your healing fury there. Go back to the tank, cast disable on the opressor and you should have time for at least landing one heal. The tank will topped due to sinastry.

If you are having mana issues with AST, it's because you are panicking and making use of benefic II or aspected benefic more than you should. The regular benefic mana cost is totally laughable (costs far less mana than Cure and physick from the other healers) so even if you spam it you are never going have mana issues.