Since this thread seems to have arisen due to a PM I sent Cliff asking how to deal with the problem on my TV, I thought I'd post how I wound up solving it (or at least getting it as watchable as I could, given the parts I had on hand).
Here is part of the horizontal section of the schematic for my Zenith C1415 set (16C20 chassis). I have circled the two components I changed in dark blue:
I noticed that if I disconnected C47 and C48, the picture became quite stable while watching VHS tapes (with only a very slight bend at the top, depending on where I had my horizontal hold set). So in order to leave everything connected and still solve the issue, what I ended up doing was making the C48 capacitor a very, very small value and making R70 a very, very large value (currently, I have less than 10pF for C48 and more than 1M-ohm for R70). An interesting side effect is that the horizontal hold locks in over a much wider range, now. I can actually sort of use the horizontal hold as a centering control now, and somewhat control the degree of bending at the top of a VHS signal.
EDIT: I might have overdone it, haha. The picture tends to bend a bit with sudden changes in brightness with an otherwise good signal, so I think I have a little more experimenting to do.