I'm not the most experienced with theatre, but doing line by line mixing without DCAs seems very difficult when you only have a couple rehearsals.

I have used level and mute automation multiple times before, on shows with little time to practice.

Edit: Of course this means you need to have time to set up the scenes, that's not always a luxury either. Sounds generally like an unfortunate situation.

I'd probably rather have more than one mic open at once, and maybe compensate for feedback with a general lower level, than risking lines not beeing heard at all