[RichG]

Hello,
Thanks for the replies, everyone! I feel a bit foolish for not thinking about how transformers are actually constructed (probably comes from never taking one apart).  In my defense, I did say rewinding transformers was not in my wheelhouse.  The explanations made perfect sense.  I feel better about looking for a replacement transformer, knowing I'm not limited to radios but can include TVs.  I did try to bring up the original transformer on a variac. When I got to around 20 V or so, the transformer started to hum and get warm, so I gave up. It is definitely toast (no pun intended).
Brad, I totally get finishing one project before moving on to the next!!
Thank you everyone1
Rich