Some food for thought?
I support a corp site that is allowing another corp to 'share' their moodle. Great! Saves cost etc. but, every once in a while Corp B (the one 'mooching') wants to do something the hoster Corp does not. So that's a rub. If Corp B allowed to make site backups, they have all of Corp A's users and courses.
In your case, is the other Edu 'good' with you having a complete copy of the shared site? When you do get it installed, you'll have all other other Edu's courses, users, etc. If not removed, there is a chance for errant email or notifications being sent to users of the other edu. Confusion!
Option: if not too many courses ... on the shared server, make full backups of your Edu's courses. If using Linux the server op could script a command line script that could do that. You then, would, of course, have to restore all those backups to your server. But, all data in your server is your Edu's.
'spirit of sharing', Ken