I've found the chuck listing in the PSI on-line catalog. The description includes this information on the included jaws:
The picture Paul provided suggests that he is trying to use the 'Pin Jaws'. According to the description, these jaws are
intended to grip mortises (internal, expansion), although I'm sure that they can be used to grip a tenon. However, the important point to note is that there is a minimum tenon size; when the four flat sections of the jaw base (the flat plates that are screwed onto the sliders in the scroll chuck) come together, the exterior of the jaws form a nearly perfect circle that is about 1" in diameter.
At the same time, the interior of the jaws form an interrupted circle. The PSI specification doesn't state the diameter of that circle, and because I don't own those jaws, I can't measure it. But whatever that interior diameter is determines the smallest tenon that the jaws can grip.
So my suspicion is that the blank that Paul is attempting to grip at, or slightly less than, that minimum dimension. Hence, the base of the jaws close completely before the jaws can firmly grip the blank.
PSI used to publish a really handy full-page table in their hard-copy catalog that specified the gripping range of all their jaws and chuck combinations. Ah, the good old days!