I just finished a battle with my rust/oxidization and paint on the '59 Jaguar.
Oxalic Acid was the best for rust. You can soak parts in there and it reacts with the rust molecules and removes them, while leaving everything else. I put a chainguard in there and it worked great, but it did 'thin' the paint a little. Maybe not the best solution to use, and it would need to be a big bath for a frame anyway.
Maybe a little WD-40 and steel/brass wool (0000 wool), but that will soon strip down to the paint and remove that as well. I use that for more agressive polishing/stripping/
You could try just a rag and mild polishing compound (one with a little abrasive in it) used for cars. That might be the trick to get some light layers off.
Good luck and let us know how it goes.