I generally keep my dough pretty thin and roll out several crusts out on parchment paper. I do not put any sauce or toppings on the pizza until right before it goes in the grill to keep the dough from getting soggy. I believe you want the stone to be 600+ degrees to prevent dough from sticking. I have ran some pizza cooks in this temp range and when I am not in a hurry that 600 to 700 degrees is probably ideal. However, if I am cooking 10 or more pizzas I tend to run hotter so my cook times are shorter. If you really want to try to dial it in thermoworks has some IR thermometers that work well.
The only thing I have noticed that can be troublesome with really short cook times is that some toppings may not be cooked all that well. I would recommend always pre cooking beef/sausage and any thicker veggies like peppers and etc. Otherwise the meat may not safe for consumption and the veggies may be more crunchy rather than a nice cooked consistency. The steel plate that goes on top of the pizza kettle can help with cooking toppings, but only so much.
Jeez I really need to do some pizza cooks. Have yet to roll out the pizza rig this season.