I tried another approach, and it worked. The dust thing was getting worrisome, which means troublesome.
What I did was use a box cutter with snap-off blade ends to deepen the score marks that were already on the PSX board, until I had weakened it enough to snap off with the pressure I was (mentally) comfortable applying to it. Those as-delivered score marks were already quite deep, but the board was still surprisingly stiff. So, it took a lot of passes with a new knife point on each score mark, but it worked faster and safer than trying to setup a saw to handle the dust problem.
So, now on to sanding the edges by hand outside in a stiff breeze.
Thanks to all for the thoughtful inputs.