Overheating rear end

Ima thinkin.

In the meantime,
Are your rear tires and wheels matched in size?, and
what are your tire pressure back there? and
have you done a 4-wheel alignment to make sure both of the rear wheels are parallel to the centerline of the car? and
Ok my brain is waking up
You said;
"I only reused the 9" drums. Shoes, hardware, master and wheel cylinders, all new."
My guess is that you also swapped on, the 9" backing plates.
You didn't mention unusual noise, so my guess is that the sides of the shoes are NOT rubbing on the drums, as if
the shoes were the wrong width, or
the backing plates were the wrong offset,
or the axle "hubs" were too short, or
Somehow the axles went in, too deep into the tubes.
or simplest of all, the drums are just shaped wrong.