Originally Posted by
ilmaestro
I had looked at naval jelly, but I can't find anything definite that says it's safe for surrounding paint.
Well, both navel-jelly and oxalic acid will cause problems with the paint. That's because they will creep sideways under the paint and work on the rusty metal underneath the paint, resulting in loss of adhesion. Or in the case of oxalic acid, just metai will do. In either case, you want to tape off the paint and leave just the rusted spots exposed.
The problem with this kind of rust is that it's pervasive and rust in anaerobic conditions (under paint) will actually spread faster than exposed rust. Most likely in your case, it'd be best to strip the entire frame, remove all the rust with naval-jelly, sand, primer, sand some more and paint.