I, too, have been wracking my brain to find some way to game the existing settings. I'm still not getting what I need, but I think I might be able to describe the problem and solution in a way that a software engineer or interaction designer might understand.
The problem: Someone books one or more days during the week, with a checkout on Saturday. That splits the weekend, which effectively makes the home unavailable for a majority of potential weekend guests who generally want to book the entire weekend.
Setting two-day minimums for Friday and/or Saturday doesn't solve the problem: A guest can book Saturday and Sunday nights, or Thursday and Friday nights, thus splitting the weekend.
Blocking Saturday check-ins doesn't solve the problem either. A guest could still book Friday night and check out on Saturday, thus making Saturday night entirely unavailable.
The solution: No check-ins on Saturday. Any guest who wishes to stay Saturday night must check in on or before Friday night. The key condition here is "on or before." We already have the option to stipulate a Friday check-in, but that just prevents anyone from checking in on, say, Wednesday or Thursday from staying through the weekend.
C'mon Airbnb, this really isn't such a unique or unusual request, much less a difficult one to code! This should have been available years ago.