Don't think there is a work-around for it.
Realize this response doesn't solve your problem but ...
Here's a thought ... why is provider allowing users to install or attempt upgrade to an existing Moodle IF the requirements for DB changes mean super user priv's? Sounds like provider might not be 'moodle friendly' enough.
Another throught ... question to ask of your provider. Can a customer have shared hosting plan (just for the code and data) *and* opt to run a dedicated DB server where customer could then be 'super user' and make such changes the DB for Moodle? That would cost more and present you with a learning curve, but might be cheaper than the only solution available to you at this time ... which is a VPS.
If they won't do that, then Emma is 100% correct ... only alternative is to upgrade to a VPS.
'spirit of sharing', Ken