I’d probably cut it all off rather than try unwinding it to get back to the iron core. Seems though that it’s way out of reach. I don’t own a lathe and even then I’d need to make the jig and buy the wire.you will first have to cut the outer case away that may or may not have part of the coil melted into it then you will need to unwind every bit of the copper windings to get to the center of the coils primary winding, recoat the primary then rewind the secondary using lacquer coated copper strand but beware if any abrasion happens you start over then it will require potting the copper in place and recovering the outside. even at 100 bucks to replace it my time and frustrations are far more valuable elsewhere.
Thanks for the info mate!In the early days at the National Research Council, we used to wind our own transformers, coils, solenoids, etc. Had a special room equipped with coil winding equipment and a trained operator who did nothing but wind these things. An exacting task by someone who knows what they are doing, not something to try by hand unless you are totally obsessed with doing it.