The mechanic does about "your HP" in damage, which means any shield will essentially be your new HP after the mechanic hits.

What I'd recommend is a Recitation Adlo on a tank and spreading it to the party before the mechanic hits. This will reduce the healing burden on the entire party by more than a Succor and massively reduce the healing burden on the targeted tank.

If you want to handle both tanks on your own, you can do something like this:
- Tank 1: Recitation + Adlo for a massive shield + Lustrate
- Tank 2: Excog + Aetherpact (you'll get 3-4 ticks during the 10s doom).

This will easily take care of over 40k HP on each tank. The rest will be handled by any aoe healing you and your co-healer do.