Replacing the damper diode didn't help the hourglass distortion, but it did increase my horizontal deflection signal by quite a bit. It was definitely weak. For some reason, this actually helped to make the picture look noticeably sharper, so that was worth doing.
I found what I think is the problem with the geometry now. There is a coil on the rear yoke assembly that the service manual calls "PIC". This is connected in parallel with another inductor and then in series with the main H Yoke. The PIC inductor is wrapped around a plastic ring and placed around the rear of the yoke. The other inductor is a little guy that is mounted next to the main front yoke.
I found that the PIC inductor is low by about half. It's supposed to be 0.48 ohms, but it is about 0.22ohms (taken out of circuit). After looking at it carefully, I realized that it is stuck in place with the same brown glue as was on the rest of the PCBs and had gone conductive and corroded a lot of the capacitor legs and stuff. I got it off of everywhere else but here.
Here is the yoke I'm talking about and the position in the circuit from the Sams.
Does anyone have an idea how to remove the glue from this inductor without ruining it? I don't easily know how to replace it, and any original part would have the same brown glue on it.
I was able to remove the rear yoke assembly and at least remove the inductor wires from the glue where they join together at the terminal strip. This raised the resistance from a consistent 0.22ohms to a consistent 0.26ohms. The brown glue is all up and down both sides of the coils, so I am fairly confident that this is what happened with the spec of the coil. I don't know if this will actually improve the hourglass distortion, but the inductor appears to be labeled as something that controls the pincushion correction, so I'm hopeful.