[BrendaAnnD]

Is it the output primary opening up, or the choke section? Either way, I would check the cathode current of the 35L6 and make sure it isn't drawing excessive current. For this purpose you can just sub in a cheap filament transformer (either 6 or 12 volt secondary will do, you don't need hi-fi for the current check).

Transformers for 50L6/35L6/50C5/35C5 are just about universally interchangable, and I'm pretty sure I have, if not a new one, then a good used one in my stock I could send you. Dimensions are more critical than most other considerations in this case.