Chris
I don't know whether this is relevant.
Nothing to do with headstock 3-jaw chucks, but I had a similar problem with the Myford, so I'll stick it in anyway.
I had a useless Chinese drill chuck with this fault. Don't know brand name 'cos it didn't have one.
Why doesn't that surprise me ?

Took ages to suss out what was wrong, it ain't obvious, but the 6JT socket was not axial. Not by much, but it made a hell of a difference.
Paricularly on small holes.It gave erratic results as the arbor can go in the tailstock at any angle. So, the error differs each time.
Dave BC