I have actually started taking a liking to skipping the stone first, let me explain. The last couple of times I did pizza I went ahead and put the dough directly on the grate for about 3-5 minutes, directly over the hot coals. This gave the bottom a nice browning with bits of char that we've come to enjoy from our favorite brick-oven style pizza joings. Then, once that first side is done, I pull it off the grill, flip it, top the cooked side, and cook the 2nd side directly over the coals for about 3-4 minutes. Once I've gotten what I'm looking for there, I transfer to the elevated stone so that the toppings get nice and melty. A couple of extra steps, but I find this gives me the best results.