I'm considering doing something similar. Instead of using a perforated pizza pan, I'd like to substitute a pizza screen.
You mentioned your pizza cooks in about 5 mins. Do you know what the temperature of your grill is?
I can only guess that the temperature at the tiles is well over 500* but how much over I don't know. The grill lid has a temp gauge that will read over 450* on a hot summer day, I imagine if left with all burners on high for an hour or so it would easily reach 500 but I also would think that the temp on the stones is considerably higher. I would like to invest in a infra-red thermo and maybe I will put it on my wish list. Further I have considered buying some thermal blankets to throw over the lid and also cover the opening in the back, although I have some concerns that it may actually overheat the entire unit and I don't know what the results of that would be but that would certainly add an additional element in getting and maintaining a higher heat level.
In the end however, I am dreaming about a wood-fired oven in my backyard so I need to consider just how much success I want to achieve on my grill.
PS. I would think the screen would possibly work even better than the pan since you will be that much closer to the tile surface. I acutally have cooked a few pizzas directly on the tiles and they came out exceptional. The only reason I don't do it on a regular basis is my grill surface is a little small and I can only get two 12 x 12 tiles to fit. Therefore using a 15" pan on top is not a problem but sliding a 15" pizza on top of 12 inches of stone just won't work.
Good luck and let us know how it turns out.