I'm not looking for page protection, I'm looking for a universal permission to disallow anyone that's not a local staff member from moving/renaming pages

No, something like that doesn't exist to my knowledge.

You should only protect a page from being moved if that page has experienced a lot of vandalism. You shouldn't stop a page from being moved because of vandalism that hasn't happened yet.

If there is a serious problem, and this is necessary, then it can be done by staff. We tend not to do it in general though, usually specific protections are enough

Interesting that this doesn't already exist. I don't see why regular users would need to completely rename and move pages.