Henry's Cat, it was amazing that you posted this since I was just going to ask about a solid state rectifier. My idea now is that my trouble was not a bad rectifier tube per se but rather a problem that lead to the destruction of my rectifier tube.
Progress today: after redoing some bad soldering (shame on me, I know), I had both Quad II's playing. One, with an undamaged (as far as I know) rectifier tube, behaved nicely, sounding good. The other, with a rectifier tube probably damaged by the bad soldering, acted somewhat strangely. It came on and was playing nicely, but twice in six minutes the rectifier tube flashed brightly--white light--but kept playing, sounding like an LP surface defect, quick recovery. It then played for ten more minutes, and then blew its fuse. I didn't want to put my one remaining undamaged rectifier tube in before consulting this forum for advice. So I'm maybe halfway there, maybe even closer. One amp seems just fine now.
Here's what Tube Depot says about their solid state rectifier:
Note: Please be advised that this replacement will increase overall B+ (plate voltage) by 10-20%. If your filter caps are older than 20-25 years, we suggest you replace them before installing this solid state rectifier.
I'm not sure which the filter caps are, but I changed every cap in the amps, so none are too old. Can I safely go ahead and order a pair of their solid state rectifiers? I'll wait to hear. I'm sorry to have been such a basket case with this Quad II restoration project, but grateful for all the help I've gotten.