I have one of these stones, and I use mine as the hearth in my LBE. The soapstone holds the heat amazingly well and does an incredible job tempering the heat transfer to the crust so that the top gets done at the same time as the bottom. YMMV in a standard, unmodified gas grill though.
For starters, put the pizza stone on the warming rack and try the soapstone as the hearth. Preheat the grill to 80% of desired temp, measured on the hearth, turn it all the way up and launch your pie.
You can improve your grill's performance as an oven by using foil to block the cooking grate except for a passage in the rear, under the top stone and cutting a closable door into the grill hood for increased air throughput. Just cut a rectangular 4"x6" area in the front - retain the cutout and put a hinge on it so you can close it and use your grill the regular way as needed.
Good luck, and post some pics!