radio shark, forgive me if you already know about this.....a restaurant in rhode island called al forno cooks their pizzas on a wood fired grill at high heat. They were the first in the area that I know of to develop this method, and now years later its popular at many restaurants and pizzerias. They do it a little differently by using finely grated cheese and a sauce that is warmed in a container on the grill. They cook one side of the skin, flip it, then quickly put down the cheese first then sauce and other toppings after that. The pizza is phenomenal. I think your method is also a great way to make a pizza, and I'm sure produces an excellent pizza! If you want to try going the whole way on the grill like al forno you might want to experiment with a large lid that can go over the pizza after the flip to contain some of the heat and get the top cooking a little more. I have done this successfully with a modified saute pan (handle removed)
It's good to know that others cook their pizzas on a grill. I started out grilling both sides of the pizza, but I prefer a traditional pie with a nice puffy cornice, something you just can't get by grilling both sides. I've thought about the top heat issue many times, when I first started I would cook everything on a grill pan before cooking the pizza, then basically just grilling until the cheese melted. Sorta like what you mentioned, I've thought about taking a cast iron pan and cutting off the handle, preheating, and using it as a hood. I'm not sure that would even be enough to brown the cheese though, and you'd really have to be a wizard to get consistent results outside. The broiler has worked perfectly, so perfectly that it feels like I'm cheating on something. When you first go looking for info on home pizza making, you usually find recommendations for pizza stones or steels, even for outdoor grills. My setup is laughable, it's a Weber Q and I finish in the oven on broil.
I would recommend this site to anyone wanting to learn pizza making. Forget buying books, this site/forum is more valuable than any book ever published.