Caustic is good at killing rust. However dipping your whole frame might be a bit tricky - you could always do it in the bath and leave it to soak for an hour. As soon as it comes out you'll have to dry it and then coat it with something to stop it corroding again.
You'll also want be careful with any caustics cause they're pretty nasty if you get it in your eyes etc.
Bilt Hamber - Deox C seems quite popular amongst automotive restoration people, might be worth a try but i don't think it's particularly cheap.
It'll prob be quite a long time before you see any significant structural problems with rust.