The problem went away. Perhaps is was a PHP caching issue on the server?
Well… I’ve re-activated backwpup on 2 of the sites I had disabled it on, and now it all works together. Maybe there’s something being cached in the file system of the host when changing versions of PHP? It definitely was breaking, but now seems OK.
I did not get a notification with your first reply. I don’t know what else to add to my original message other than what I already did. I can do some more tests to see if anything has chagned.