One and a half of that dough recipe makes for reasonably thick crust pizza and about half the oil baste covers about two pizzas.
Stretch the dough out onto a piece of wax paper on a tray, then coat with the oil. Flip onto the grill, then peel the wax paper off. Otherwise, the dough sticks to the tray too much for a smooth transition.
Brush the second side of the dough as soon as you put it on, then cover and cook until you're able to flip it onto the 2nd side. We don't cook the first side any more than necessary, and then try to leave it longer on the 2nd side to heat the toppings.
Toppings go on and we cook it until the cheese is pretty well melted. That seems to be about the right time for the crust, but we weren't satisfied with the warmth of the toppings, so . . .
We found a better plan is to preheat the oven to 300 or so, then put the pizza in there until the cheese looks right.
We've only used charcoal fires in a kettle grill, which need to be in the medium-low heat range. Any higher and the crust burns before the toppings warm through and we want the charcoal to work it's magic. That makes the oven kind of a safety net because if the fire isn't right, we can always leave it in the oven a little longer without burning the crust or sacrificing the great taste the charcoal gives.