On a hunch, I instead opted to change Upload Url Path (of the main site) to point to where Fileupload Url already was pointing, and lo and behold, now the uploads get url’s with a /files/ base (which I feel is best).

Funnily, despite this same setting on the testing site, the url’s there have the wp-content/uploads base (like I mentioned in the previous comment), as if Upload Url Path didn’t have an effect. There doesn’t seem to be a Fileupload Url setting there — perhaps it’s deprecated? (The testing site runs trunk, whereas the main site runs latest stable.)

(Usually it’s the other way round: something that works in testing won’t work on the production site.)