I agree that it's at least quite plausible (as per your post, it's not proven to follow from GR) that if the universe spun around you, it might be exactly the same as if you were spinning. However, if there's no background at all, then I'm pretty sure the predictions of GR are unambiguous. If there's no preferred rotation, then what do you predict to happen when you spin newton's bucket at different rates relative to each other?

EDIT: Also, although now I'm getting a bit out of my league, I believe that even in the massive external rotating shell case, the effect is miniscule.

EDIT 2: See this comment.