1971 Demon Strange steering problem

Another thing I have seen is when almost any part in the steering system is NOT rigidly fixed; as in any item that can allow the steering on one side of the car, to move out of synchronicity with the other. I took it for granted by your statements, that this was NOT happening.
Like if,
the centerlink is NOT held in it's place, say by the idler arm flexing
Or the Tie-rod connecting tubes are loose,
or the UCAs are moving in the saddles.
or the steering box is not fixed.

But the pivoting force has to exist prior to that, and the only force I know of, with the wheels steered ahead and the suspension not cycling, that can do that is Scrub radius.
Excessive; caster/SAI/LCA angle, or broken/missing shocks; can make it worse.
here is a link;
Scrub radius - Wikipedia
What Is Scrub Radius And Why Is It Important?