Help with big pulls in newer content

[tinythinker]

I've been away a bit but did get to i289 and do a clear of Ala Mhigo before that. I got back on my WHM and today is my second day of roulettes. One thing I've noticed is that in Bardam's Mettle and Ala Mhigo I am awful with the large pulls, so I'm going to have to say "no large pulls please" for now.

I get that a well-timed Regen, an Asylum, even a Divine Benison can help. And yes, Holy has a stun, which can contribute to mitigation. But, the tanks drop so quickly. I am using up Benediction and Swift Cast (for a Cure II) so fast. So I end up mostly just trying to heal because otherwise it's a wipe.

And yes, from what I can tell the tanks I've played with seem to be using Shield Oath, Grit, etc.

I just can't cast fast enough unless I use Presence of Mind, assuming I can stop chain-healing long enough.

I don't claim to be a great healer, but I do my best. Is there some obvious combo or rotation that I'm missing or do I just stick with 95+% heals for those runs? I don't mind mostly healing or I would pick another job. Just wondering what else to try.