Latest chapter in the Saga of Sven

[veg-o-matic]

Hello, all:
Youall are probably familiar with my good friend Sven, the '65 Zenith model M2737U, subject of a recent thread.
Well, he's feeling fine now and brings in a jolly decent picture. This is using rabbit ears in an area I was told couldn't get decent reception. Must have one hell of a tuner in there!
Anyhoo, I connected him up to a VCR so I could use the remote control and the picture is still fine 'n dandy. Unfortunately, when I play a tape, the picture ain't so good.
At first, there were blank parts of the screen at upper left and lower right. Fiddling with the horizontal hold knob took care of that. Still, the upper half of the picture is significantly bent to the right. I looks like someone is pulling the picture over. The picture on the bottom half of the screen is perfect.
WTF?
Naturally, I tried messing with the fine tuning but that didn't seem to help. In fact, it didn't seem to do anything at all, so I'm not sure it even works.
Anyone got any ideas? Is this a common problem with older sets? I seem to remember that being mentioned when VCRs first came out.
Thanks again for your help!
Bob