I believe I found a solution.
I copied the HTML from the “404” page and pasted it into a new page. Published the new page. Adjusted my site’s menu. Loaded the new page in a browser with Inspect Element / Network – check that the new page’s GET (html) now shows 200, which it does. Rinse and repeat as necessary. Delete old pages permanently. Redirect Adwords campaigns. Watch them change from eligible to approved. Pop cork on champagne, at least for tonight.