Our TV is a '73 Zenith 25CC25, so the DVD player has to play thru a
cheap RF modulator from MCM onto channel 4. Right now I have no way of
knowing whether the problem is due to the player or the modulator

Try using the player on a different television.

If this symptom does not exist when played on a different TV, then the problem
could be with your 1973 Zenith set or with the MCM RF modulator.

To test the modulator, simply try it on a different TV. If it checks out okay,
you may want to consider getting your Zenith checked out, primarily the tuning.
You may just have to squirt some tuner cleaner in the tuner parts since I
doubt your TV has automatic electronic tuning. - Reinhart