ok, thanks. 1 and 2 was worth a try. 3 does sound like a short interruption, although it would of course be nice to avoid it.
Test:
So you can almost "predict" the downtime and see the spike building up in your admin panel, right?
What if you tried to put the sites in maintenance mode (and log out of each one) around the time the downtime usually happens?
If you do this only for one site at a time, you could be able to elminate the one causing the error (or confirm that all of them are responsible).