Hi,
I owned also a ZX-81 (24 years ago). As far as I remember, TV image was controlled by the Z80A microprocessor, not by an specialized chip. It's possible that syncro signals will be OK for a TV-set but unstable for other purposes. Try to get a time base corrector (TBC). Some high-end VCR has TBC and also exists as PCI cards.
Good luck
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