So, my experiment to forego the rolling pin worked beautifully.
I used bench flour to keep the dough from sticking and merely tugged and lifted the cold dough, stretching and coaxing it into a thin skin, much like any delicate high hydration dough. The dough was very extensible and it fights me fromone direction, but not the other, so it's easier to let it become a rectangular pie rather than try to force it into a round shape. Baked 6 to 7 minutes at 550 directly on stone.
These pizzas were just as delicious and delicately crunchy as before, able to hold a bunch of toppings, with half the effort of my previous bakes.
I sure do miss pepperoni.
you can see which halves are mine, and which are not.