I finally got around to doing this today. Ken, you were absolutely right, it was a K7601. Did a cap kit and put in a new flyback, which put my focus range back where it should be.
I still have focus problems, though. With the brightness way down everything looks super crisp, but as I turn it up, the brighter colors on the screen get fuzzy. White text is particularly bad. I've tried different combinations of "screen", "brightness", and "contrast", but I can't seem to improve it. My oscilloscope is not really accurate enough to do a proper white balance procedure, so I'm just guessing on the "screen" control. Does any of the horizontal stuff have an effect on focus?