i can't see much evidence of rust growing under the paint in these pix, but assuming you do see such and want to take another route to arrest it, maybe...
clean the entire stripped frame and fork, then get a plastic wading pool and soak it all in a solution of oxalic acid (AKA wood bleach) in warm water. That should NOT harm either the paint or the decals if done as many others have, but can penetrate porous paint and neutralize rust.
One caveat is if there's rust under chrome you can lose portions of the chrome plating when the rust holding it is removed from the steel. Often that will be minimal but "it all depends"

Then rinse with clean water and DRY it thoroughly, use a hairdryer or heat gun to drive all moisture out of the innards, with skill and luck you'll then have a frame with no rust ready to grow again BUT you should protect the insides with favorite "Framesaver" type fluid and then follow Velo Mule's guidance for treating the outsides.

I bet it will turn out great!