Oh, pardon! I couldn't know, that I was talking to a big fish. ;)
Well, the big fish deploy web server clusters, and often reserve one node solely for course backups. My humble solution still makes sense, if you replace "your PC" with a server in the IT. Doesn't have to be very powerful, a VPS might do, only the database has to be fast. Between two course backup cycles, typically 24 hours, it has to sync itself to the prod. server er, then finish the round of course backups. One needs to streamline the process, with rsync on the syncing side, an efficient course backup strategy on the backup side.
I know the underlying problem very well. With the size of the site the course backups get slow, consume so much resources that the backup process interfere with the normal operation. What I don't know, what if the course was active, files being uploaded, during the backup?