I'm fairly new to endgame AST but here's what I do in those situations:

On big pulls when a tanks gathering up trash like that I follow behind him closely and right as he stops Ill swiftcast Aspected Helios followed by Aspected Benefic to stack HoTs then pop Synastry for the regen boost, start casting benefic II (hopefuly its a free proc!) (or Essential Dignity if its dire) to top off the tanks life pool you know is down at this point. Hopefully he's still alive, and if the damage is still coming in crazy hot, pop Lightspeed and chain heal at speed. Once your 58 you can throw up Collective Unconsious after your top up heal to stack yet another HoT and some damage reduction if things are really hairy.

Lots of AST's shy away from Aspected Helios for mana conservation reasons but if you use Luminiferous Aether proactively (I pop it first around 80%) I can keep it up for most fights.

If your even a little bit worried about about the tank spiking damage and dying, I wouldn't worry about dps. Everyone's dps is going to be down if we let the tank die, so my focus is on that, and I'm only dps'ing excessively when I'm running something I'm comfortable with. Otherwise its just DoTs and Malific II when I can spare the cast time. The meager dps we add isn't worth trading stability if there's any risk involved, imo.