Results: not bad, needs tweaking. The stone in fact fits perfectly: it fills most of the grill's surface (it's a small grill), while leaving a little room around it for airflow. As expected, my good newish infrared grill gets Hotter Than The Blazes of Hell (a solid 600 degrees): the pizza that traditionally needed 11-12 minutes in the oven was slightly overcooked on the grill in 9. So it looks like, with proper preheating, I want about 8 minutes for my usual thin-crust pizza. And in many ways the grill is much easier: I'm not bending over to the oven, I have easy access to the top of the pizza if things slide during the snap, and I'm not worried about crap falling off the sides onto the floor of the oven and burning.
The one thing that worked poorly was transporting the pizza. I have a fairly cheap wooden peel -- good enough to snap the pizza *on* to the stone, but too thick to easily get it *off* again. So I traditionally just grab the stone with my trusty Ove' Gloves, and pull it up on top of the stove to cut. But of course, the grill is out in the driveway, which is a *long* walk -- enough so that I began to burn my fingers right through the freaking Teflon. So if I continue to do this, I may need to invest in a thin steel peel, that can easily take the pizza off the stone when it's done.
The recipe needs work: we tried a sauceless pizza, largely inspired by some freshly-bought Chipotle Olive Oil from the lovely place we found down in Providence. The results were tasty, but the flavor of the oil is pretty mild, and the pizza was generally too dry. Consensus was that, if I do a sauceless pizza like that again, I need to double the sliced tomatoes on top.
(Kate's suggestion for next time is a Fajita Pizza, using my now-perfected Pico de Gallo as the "sauce", some southern-style ribs, pregrilled with a good rub, as the protein, and Poblanos for the veggie. That sounds good enough that I might try it next week.)
But overall, enough of a success that I suspect I will get back into the groove of making my own pizza. Doing it on the grill is slightly inconvenient from a transport POV, but being able to run something *that* hot, especially without overheating the kitchen, is really nice for this purpose. And pizza! Mmm...