'nuther thing about pizza
If the stone or deflector is too big, the bottom will burn before the top is cooked. Friend got a stone for his grill (electric grill, but we won't think about that), and put a stone on it. There's very little space between the walls of the cooker and the outside of the stone. So, the stone gets nice and hot, but there's little dome heat, especially when one opens the top to put the pizza on. All the dome heat escapes, and it can't reheat in time to cook the top of the pizza before the bottom blackens.
It's not pretty.