Okay, thanks for that guys.
One clue that might assist in tracking down this problem is that the
aforementioned arc that appears at about '37 minutes past the hour' on
the outermost polar circle when the 50 ohm termination is fully screwed
in first begins to appear at just before 12 o'clock and gradually
circumambulates around this outer circle anticlockwise to its final
position as it's fully screwed home. I'd have (intuitively) thought
that once the centre pin makes proper contact with its counterpart, the
trace would suddenly flick to close to the centre. But with no
experience of VNAs, that's just a hunch. Any suggestions?