Hey OP, I think something that could help with all three healers is skill stacking. I’ve seen it mentioned a couple of times but one thing to keep in mind is that if the tank is doing larger pulls, you will have more time to get those cooldowns back.
On Scholar, stacking Fey Illumination and Whispering Dawn ends up being pretty strong mitigation. On White Mage, Regen and Medica II. And on Astrologian, stacking Aspected Benefic with Celestial Intersection(no matter what sect).
Maybe see if a tank friend or a tank in your FC can run a few dungeons with you to help you practice that.
And the last bit of advice I can give(something I struggled with myself) is to not be afraid to use cooldowns :) the longer you save them, the more opportunities you passed where they may have saved a life.
I hope these tips helped!!