Options.
Reduce gain on his mic.
Reduce his monitor volume.
Reduce the amount the mic picks up of the monitor relative to drummer vocal. Is he getting right up on it?
Unfortunately putting the monitor up higher to allow it to be turned down also puts it closer to the offending mic. Directions, reflections, and the pickup pattern of the mic are what you have to figure out. I think I would be sacrificing some stage area to put the monitor directly behind the drummer so he is a big meat baffle for the mic.
Juggling gain mixer to FOH like that doesn't help feedback per se. The juggling needs to happen at the mic inputs. Anything you can do to get more of what you want to go into the mic with less extraneous racket allows higher gain on that mic.
Dialing back the whole band right back on stage and putting it all through the PA would. Guitars on IEM for the win?
Since you are good with IEM the big thing you can do is trade bass cab for FOH sub and put very highpassed bass in monitor for drummer.
I dunno, they claim to want to sound good. Somethings got to give for that to happen.