Definitely need to put the pizza stone in with the coals, so it can be at temp when you load the pizza. I load it all raw with a home made pizza peel, no pre-baking the crust. My go to ingredients cook pretty quick, such as fresh mushrooms, sardines (!), onions etc. - no raw meats. My pizza boils and bubbles on the top in the center before I remove it. My pizza is pretty thin, definitely not deep dish!
G