Jon, the principles governing a broiler drawer stone approach are no different than those governing a broiler drawer plate approach. There may be a distance that will allow the broiler to sufficiently pre-heat the stone, while not burning the top of the pizza. On the plus side it sounds like your broiler stays on for quite some time if your oven is making it to the 700s.
But, yes, moving a hot plate isn't an option. That's why I talked about the safety aspect earlier.