After looking over my new Anti-Monitor rules, I realized it said he was free to push as much as he wanted, and ignore the damage dealt because of Quintessence. I didn't remember reading this in the Starro insert; did I miss something, or is he only allowed to act two out of three turns?

You missed something, he can act every turn and doesn't take pushing damage.

Ah, see, I missed the "can be pushed even if he has two action tokens". Thanks for that.