[old_tv_nut]

If the horizontal sync phase is the problem, suspect the phase detector X14 and the components around it.

If your scope is dual-trace, connect one probe to X11 (AGC gating pulse) and the other probe to the video detector output and see if the pulses line up and don't move with respect to each other with changes in video content etc. Make sure your scope is triggering on channel 1 only or channel 2 only.