sonett - full rear brakes rebuild, new front rotors and pads
I was getting extreme vibration when braking. And also vibration when above 60 MPH even when not breaking. It felt like my wheels were way out of balance. Turns out it was extremely warped front brakes causing both problems.
I replaced both front brake rotors and pads. Then I thought that maybe the fronts were worn so badly because the rear brakes weren't working. I have never actually been in the rear brakes in the entire time I owned the car.
So I did a full rebuild on the rear. I cleaned up the drums and had a shop machine the braking surfaces. I installed new wheel bearings and seals, new shoes, new hardware, and new brake slave cylinders.
I am happy to report that braking is now smooth and the vibration above 60 MPH is gone.
I am reasonably sure that the old rear brakes weren't actually doing any braking. The drums were rusty. The shoes had pad life left. It was when I was removing the drums that I saw the rear brake adjusting screw. Turn it in to tighten up the rear brakes. All the other car drum brakes I have worked with, which isn't many, had an auto tensioner. This one is manually tensioned. I likely just needed to apply some more tension to get the rear brakes working. From now on I will check the rear brake tension at every oil change to avoid this situation again in the future.