Just a heads up re pizza on the grill. I have a Napoleon grill, gets very hot and has a lot of headroom. What this means is that the grill surface gets superheated, but the area just above it (when blocked by food) does not -- it's hotter higher up.
First time I tried to grill a pizza on a pizza stone, the bottom charred to a crisp in about 1 minute, topping was not cooked. Second time, I backed off on the heat, and the bottom charred in 3 minutes, topping not cooked. Solution was to raise the stone on tin cans.