Grilled Pizza Extraordinaire - Chef Larry Anderson, Remke Bigg's

Grilled Pizza Extraordinaire
½ to 1 cup of your favorite sauce such as alfredo sauce, pizza sauce, vodka sauce, cheese sauce or even pesto.  The pizza sauce and toppings are interchangeable it's a great way to use up leftovers!
Olive Oil
1 ½ cups Meat toppings, pre-cooked (Rotisserie chicken, precooked chicken sausage, pork sausage just to name a few of my favorite things.
1 ½ cup Veggie toppings, sautéed just a bit. (Peppers, onions, spinach, asparagus
1 cup Cheese
1 Premade pizza crust, Mamma Mary's is the brand that I have been using, it's between a thin and pan, with a little bit of a side on it to hold all your goodies in.
With the size of your grill, what might work out well for you is to grill the crust, then finish it off in a 400 degree oven for 10-15 min, or until the cheese melts.  But if you can, slide the crust far enough over so the first burner doesn't get too much heat. Check this by before you light the grill, put the crust on it and see if there would be enough room. 
Pre heat half your grill. 
Take the pizza crust, top side, and either brush on olive oil with a brush or lightly pour it on and move it around with a paper towel so you have an even covering. Place this side down on the hot side of your grill.  If it flares up a little it's ok, it's the oil burning off.  Grill it so that you see some nice grill marks on the crust. The edges will get a little darker than the center, but that's ok too.  You'll be able to pick up the nice grill flavoring off that.
Pour on the sauce! If you like more sauce, cool, you can put as much/little as you like. Add your meat/veggie toppings, add cheese and place either back on the cool side of your grill, or in the oven.  Heat until cheese is melted.  I typically don't brown the cheese like I would a traditional pizza, sometimes the crust gets too done if you do.