I would imagine that basketball would end up doubling up in your division (10/8 games) and a game against everyone in the other (5/6 games), then 4-6 true OOC games. I doubt you'd have a full 11-team basketball conference if you're recognizing the need for a split in other sports.
That would definitely work too. My only point with the single round robin is, as far as tournament goes, it's not quite as big of a disadvantage for a Napoleon to play and lose to a Whitmer or Findlay. Football that means no points and the potential for a blood bath. Basketball the smaller school can compete a bit easier and if anything, the "tougher" schedule could help with seeding.
But a double round robin in the division, 14/13 games depending on which side you're in would work as well as now that you say it, I agree is more likely.