One move Ive been leaning on for years, OP, is when it comes time to cut a few tunes with everything going, Ill remind the band that while they are playing songs its my time to keep my head down and focus on the FOH mix. Well make monitor changes between songs. Lay down the law. You are driving. If they ask for something during a song, ignoring your established workflow, give the offending party a thumbs up, do nothing, and file their request away until the song is over.