I can't comment if you are using a gas grill. I have made pizza on a Webber Kettle. I put olive oil in the bottom of a 12 inch cast iron pan and place the dough in it. I then pushed it into shape with my fingers. The dough was a standard recipe pizza dough for a thick crust pizza. I let it rise a bit, topped it with sauce and toppings, and placed it directly over the charcoal, hot and laid out as a solid bed. I put the lid on with all vents open on the bottom and top of the kettle. The crust and toppings came out perfect. I was so pleased. I have had poor luck trying to make a home made pizza in the oven. But on the grill, it comes out perfect. Also, the smoke from the charcoal adds a tremendous flavor, especially to the crust. The pizza didn't have the texture of steamed dough. It came out like great pizza crust.@Dave, the new york times' pizza dough looks more like a toast or pancake to me, but if i make it thinner, possibly it will still work too.
@goodweed, if you cover a pizza dough over a grill , would the water from the pizza and other ingredient probably make a steam and make it become a steamed pizza?
grain back in the day my sisters use to make mini pizza's with Thomas' English muffins on a frying pan.
Dressed up properly they tasted like the real deal.