Sounds like backups process/procedures need reviewing/tweaking.
For moodledata ... large as it is ... have found progressive rsync to be the fastest. Basically a mirror .. rather than a tar ball. And to a directory that could be mounted in a pinch. Actual tar ball archive happens during non-prime time especially when students wouldn't be taking finals (finals week always an exception).
Some communications between DB server and Moodle so that Moodle is put into maintenance mode with an informative screen for users. DB backups (sql dumps) should probably lock DB and prevent any admin/teacher/student access to Moodle.
My 2 cents.
Glad you have it sorted though and thanks for getting back!