Transformers may burn out due to moisture or an internal fault, but most often it is the external circuit (and here, a lack of proper fusing) that kills them.
Vern Tisdale did offer a new replacement, but they seem to be out of stock now.
http://www.verntisdale.com/Seeburgpage.htmYou might inquire if he plans to restock or knows of anyone else offering them.
I've used transformers from LPC control centers. However, they lack a filament supply (6.3V) for a tube amp and a 5 volt AC for decorative lights. I use additional transformer to supply those voltages.
----Most important is to find out why this tran smoked! Most likely it was due to an un-rebuilt selection receiver w/shorted capacitors or bad 6X4 rectifier tube.
This is why old electronics MUST be rebuilt and carefully tested before given full line power and use is attempted.
Given the amount and intricacy of the work involved now I suggest sending the unit for repair, or buying a different selection unit that has been rebuilt and tested.
Neither of these options are cheap, but that is where things stand.
Rob/NYC