You've not mentioned your operating system ... do know that there is an issue with backups of courses over 4+Gigs and it's not Moodle code ... it's operating system support for the copy command. The backup .mbz that is built in moodle/temp/backup/somecontenthashedidfolder/ is copied ... not moved ... to the course backup area ... ie, back into filedir somewhere and/or to the alternate directory for automated backups. It's the copy command on CentOS that lacks support. They say it can be fixed ... if you want to re-compile the kernel. Uhhhh ... no thanks!
Got a big backup box of some sort that you could mount a folder upon from the Moodle? Could use that as your alternative backup area. Mount Point could then also be symlinked in Moodle's file system repo in some courses so one could still access those backups ... even though they are no longer in moodledata.
Might have to increase PHP limits on time for a script to run ... as well as memory used by a script.
If you are running automated backups on cron job, switch it to manual. One could then write a small script using the moodlecode/admin/cli/auto_backup.php script (read the comments in the script) and then call that script via cron job (not Moodles) to execute at non-peak days/hours.
Anyway ... there are issues. Solutions are not 'one size fits all' am afraid.
'in the spirit of thinking', Ken