Just an idea, it's possible I'm overthinking it. I would volunteer to be Grand Scheduling Poobah also, in this case.
Off the top of my head, I would suggest 2x divisional games, play one other rotating division in whole per season, and then play 4 of the other 5 from the other divisions, based on standings. In this case, 1st place and 5th place don't crossover, 2nd and 4th don't crossover, and the 3rd places don't cross over.