A couple years ago, when I was on a pizza kick, the thing that worked best for me was to start cooking the dough on the stovetop on a very hot cast iron skillet. I would cook it long enough for the dough to start to change color and bubble a bit (45-60 seconds), and then make sure it was releasing from the pan. Then, I would sprinkle on oil, tomato sauce and toppings and move it from the skillet to the preheated stone, and leave it under the broiler for another couple minutes.

The initial cook on the pan got the crust going, and so the oven time was mostly focused on the toppings.