I replaced all tubes except the 50L6 and 12BE6 (they tested great) and now the FM is back! Yay!
I've got a 60-cycle hum on both bands, though. (It was always there, I just didn't mention it earlier.) As a result, the music is distorted, even at low volumes. I believe the word is 'motorboating'.
The radio was indeed recapped, but not very well. I jiggled some of the caps around and spaced them apart from one another, and that seemed to reduce the hum somewhat. If I wanted to send my radio to someone here to have it correctly recapped, who would be best?
Pic of radio:
