What happens if you disable zip compression in the backup prefs? Sometimes the zip library can get jammed up at the OS level. You’ll probably still want to have that option on if you are syncing these, so I wouldn’t consider that a workaround, but a diagnostic step. It is usually just a matter of clearing out system caches with a tool like Onyx, and doing a reboot. You might try doing that anyway since weirdness is going on. It would be unlikely that two computers were similarly effected by a zip library bug at once, but you never know.
I would also leave the Console open while trying to trigger a backup. Perhaps Scrivener or the OS will report something that helps.
If you can think of any software you’ve installed recently that could perhaps conflict.
No, that should be enough. Just opening a project changes it in small ways.