Left rear brake drum gets hot

That was my problem. The cable had just a slight amount of tension, and apparently that was just enough to push on the shoes and cause them to grab. I loosened that nut at the equalizer bar to the point where it sags down, and it made a huge difference. I thought as long as the shoes were resting against the pin on the backing plate it was all good. But today, I learned that wasn’t the case. The drums read 74 degrees and 87 degrees. You can actually touch them without burning your hand.
I've found if nobody ever screwed with that cable adjuster, the oem setting is always just fine. If people screw with it, they are trying to compensate for a flaw elsewhere. The problem is these cars are 50 yrs old, and the chances that some less knowledgeable person hasn't dicked with the brakes is pretty slim.