is there a way to move a page so that only the page numbers and footers move from left/right, but the rest of the overridden items do not appear on the pages and they just move exactly as they have been designed?
You could do it if you are willing to detach the pages from the masters. So if you select all of the pages you want to rearrange in the pages panel, choose Override All Master Page Items from the Pages flyout, then apply [None] to the pages via Apply Masters to Pages...
The obvious downside is now you wouldn't be able to do things like move the position of all the folios from the page's master, but if you think the page design is final you might be able to live with that.