Things go sideways when the disk fills up. rsync just gets called in a loop and eventually bails, but it should bail early with a useful message instead of the admin having to infer from the rsync output that things filled up.

Check before each rsync run (even in a loop) that there's space on the destination and just bail if not.. This could help us with catching a full /tmp as well, though that will still require a check before doing much of anything.

Encapsulate the check in a single function that we can call anywhere.