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At first I was looking at stone but to my understanding you want to cook the crust fast? The other problem with stone is I know
I will break it.
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It all depends on your recipe, specifically the water content. The slower the cook the more water you need because it takes longer to cook. Longer cooking time is more time for the crust to dry out. The other part of doing a pizza on a grill is getting even cooking from the top and bottom. A lot of grilled pizza's come out burnt on the bottom with the top under done to done. If the bottom isn't burnt then the top usually isn't done.
You might look at getting a cordite kiln shelf if you want a durable stone. They are made to go in pottery kilns and wont crack under the heat. They also handle temperature shock a lot better than the typical cooking stones. I have a 18x18x1.5 thick kiln shelf that I cut down to a 18x16 so it would fit in my oven.