I didn't read the entire thread, but what I did read here is different from every pizza grilling method or recipe I've read. I've never read any that recommend anything but cooking the crust directly on the grill. I made pizza for 3 of us tonight as my neighbor's wife is in Hawaii caring for her sick mother. I used a method from a special edition from Fine Cooking magazine. It's called simply "Pizza on the Grill", and it has made a believer out of me. I made the crust according to their basic recipe. I cooked it by their 1-2-3 method, using their recommended alteration for finishing in the oven when cooking more than one or 2 pizzas. I made 3 crusts, rolled out thin, then grilled at medium direct heat for 3 minutes on one side and 2 minutes on the second side. This can be done the morning of the party and they will keep just fine at room temperature. Then what I did was preheat the oven to 450, bake the crusts for about 4 minutes to re-crisp them, then apply toppings and cook for another 7 minutes. The best I've ever had, bar none. Next time when it's just me and my wife, I'll make 2 crusts (we prefer different topping combos) and do them complete on the grill by finishing them on medium indirect heat.
What I don't get is why so many here use a stone? My stone lives in my oven and is used mostly for free standing breads or focaccia, but never on the grill. I've used several methods of grilling and never used anything but the grill grate, and it has always worked just fine, only tonight's was a cut above because of using a different heat level. It was a wonderfully crisp, crunchy crust that held up to all the toppings you could pile on. The sauce recipe also came from the same source, and may have contributed much to the success of the meal, but the crust was a real hit.