Jim, time is no aid. With your sandwich, the top will never get substantially hotter than the bottom. Because of the nature of infrared heat, for pizza, the top has to be at least a couple hundred degrees hotter. In my setup, you're not only collecting the heat from below to heat the top stone, but, as the pizza bakes, the heat from below is flowing over it. With your enclosed oven, that active, convective heat is shut out.
You could, in your enclosed setup, if the walls supporting the ceiling were sitting right next to the hearth rather than on it, pre-heat the ceiling so that it's nice and hot, and then add the hearth stone later so you get that couple hundred degree difference. The heat in this kind of setup isn't very stable, so you only get one or two pies. You could remove the hearth between bakes and allow the ceiling to reheat, but handling a hot hearth can be dangerous.
How big is the weber propane grill? BTUs? If it can hit 650, it can do NY thin crust pizza.