Okay, this is some weird shit.
After replacing the HA11244 with no change, I messed around with the horizontal circuit, replacing D505, R527, the horizontal hold pot, etc with no change. Did some reading about flyback theory and learned that a bad AFC (Automatic Frequency Control) line could cause this (extreme shift left or right), I concentrated on checking that out, but not finding anything.
So, I pulled three games out so I could get to my Frogger, and pulled the newly rebuilt and working G07 out of it. Hooked it up to this tube - and got more picture, but found that it only locked with the bottom of the image at the top and the top of the image at the bottom - with 3-4 inches of black space in between.
So I messed around with it for a bit, and eventually got this chassis to do the exact same thing as the other chassis - offset way to the left.
Well, I decided to sleep on it. Today I went in and decided to take my original problem chassis and stick it into the Frogger. Perfect picture! Everything is where it should be. Hmm, I think, this means the problem has to be with the tube, yoke, or rings.
Since I don't see how the tube could cause this, I swapped the yoke (even though the original measured okay). Still get the same offset picture. Next I swapped the rings. Still get the same offset picture. That means it has to be the tube? What could go wrong with the tube that would make the entire picture be offset this much? It's a 19VMNP22 and has burn-in to indicate it's worked in the past...