Well, I'm no expert, that's for sure, so I appreciate all/any advice on things like this -- I'm more at home with solid-state devices and "regular" speaker drivers.
My ignorance has become apparent with this post; I thought that the field coil referred to the transformer, and never thought beyond that. It becomes obvious with a bit of thinking that this isn't the case, however! The original driver is gone, as far as I can tell (my folks are packrats, but the driver can't be found), but the transformer that was mounted to the speaker basket remains. Like I said, I was 15 or so at the time, and suppose I didn't have a clue as to what I was doing -- but apparently I knew that I shouldn't throw the transformer away, so I mounted it to the cabinet wall inside the radio.
In the link that jeyurkon provided, it looks suspiciously like the original driver in the radio -- is that possible? I don't have Photoshop right now (I'm at work), but if I did I'm suspecting that you'd see a small transformer mounted to the speaker basket up above, where the 3 wires from the radio are headed. That's the same configuration as was originally on my radio. Why I can remeber that, and not whether it was a permanent magnet on the speaker, I don't know.
If it was a permanent magnet speaker, why the transformer mounted to the speaker?
Dammit -- must go home and lighten up that picture!
Thanks, all -- this has been a big help, believe it or not.