Built a dim bulb tester and got the tube socket repaired.
Tester with a soldering iron plugged in:
Banderson suggested soldering fine wires to the tube leads. I did that.
I used some epoxy to re-attach the tube base. I think it will hold together as long as the connector is removed carefully.
I optimistically set up a mirror and flipped the switch! Sadly the set doesn't do very much. The tubes warm up, but there's no picture, no scanning sound, and no static on the speaker. I happened to get a phone call while the set was on and I did hear the "ba da da da da da" sound out of the speakers, so something in the audio stage is doing something.
I looked at the bottom of the chassis and everything looks totally original. Time to start the troubleshooting tree, though I'm betting it's capacitors.
-J