[Arran]

The reason I mentioned low balling if the transformer is burned, is that even a generic replacement, with the right voltages, is $75 minimum, rewinding the original is more then that. Them may ask more then that elsewhere but (A) Do they sell (B) What's the condition. I like to test transformers with an Ohmeter before I buy, the windings to be most concerned with are the H.V secondary, and the primary, the H.V secondary you can test via the rectifier tube socket, the tube filament windings rarely fail though those are easily tested as well at the filament pins of the rectifier tube, and any random tube in the rest of the radio via the fat pins. One concern with A.K sets is that many have been monkeyed with over the years, they were a collectable brand early on, so many were repaired or "restored" by previous owners, hence why you would want to look in the back.
Regards
Arran