Thanks to a generous donation from Captainclock, I received a new 3AT2 tube, AND a tube tester!
Put in the new tube, and it seems to have solved the problem! I'll need to do a longer test later when I have time but the raster came up bright!
And it looks like the tube tester survived shipping with no issues. I tried the new 3AT2 (after looking up the proper settings in the manual) and it read full emission, and the old one got up to the ? between good and bad... So I think it was marginal and finally quit.
Well, now that I have a tube tester, there's really only one thing to do: