Oh, right, I meant to talk about that.
Suplexes hit both tanks for a fixed amount of damage (the dungeon journal currently says it's the max health of the other tank, but that's out of date). They typically require cooldowns to survive. There are only three of them during the fight, at 85%, 55%, and 25% boss health. The suplexes alternate which tank is picked up and which tank is thrown at:
Prior to 6.1, you have to set up your cooldowns as follows:
Suplex 1: externals on tank 1, personals on tank 2
Suplex 2: personals on tank 1, externals on tank 2
Suplex 3: externals on tank 1, personals on tank 2
Tank 2's personal cooldowns will come back up between suplex 1 and 3, as will the externals used on tank 1. The externals used on tank 2 may need to be from a different set, depending on what cooldowns are used. (For example, hand of sacrifice has a 2-minute recharge which is probably longer than the delay between suplexes 1 and 2, but because it starts at two charges, you should be able to use it once for each suplex.)
After 6.1 you have more flexibility, but you still need to somehow coordinate about 50% damage reduction on both tanks for all three suplexes.