Ha, ha, ha! The "only" problem. I didn't know that this is for your monster site. But I remember you have dedicated a node for the cron job. That one might be able to handle the automated backups too - or not. Anyway, I don't have to tell you about the hiccups automated backups get. I have automated backups running _daily_ on a site with 2,500 courses. But on the average only about 200 change daily. Exactly those are the ones which swell weekly. That on a all-in-one box, but admittedly a huge one. The process complains about unfinished backups a couple of days and then finishes. That doesn't worry us, these are really backups, not needed unless there is an incident. How "current" your backups need to be?
About the end-users: This one is. Because teachers have the full autonomy on their courses. So, they select the mbz in the file-picker and restore. The problem is, apart from a grinding server, they will see all the backups. How selective your handover should be?