I'd like to think I'm on to something here...
Without a doubt, I have an indestructible pizza stone. If you don't want to risk cracking your stone, please do not attempt this. That being said, I figured out a pretty unique way to get Neapolitan Esq. pizzas from your grill, that requires absolutely no mods.
I took the grates off my gas grill, and removed the flame tamer of the middle burner. I centered my trusty stone above the untamed burner so the flames would kiss the bottom of the stone, and fired up 3 of 4 of the burners. After about 25 minutes, I was already reaching 700*. Probably around the 35 minute mark I was reading 850* with my IR gun
I threw the first pizza on, and the bottom was severely over-cooked at 2 minutes. I've had worse problems. Here's the fun part though, for the top, as soon as the pizza hit the stone I went around the crust with a cheap heat gun on high. I had to pull the pizza before I finished the top, but figured I could finish it off the stone and not really affect the crust in a negative way. I also used that time to hit the cheese a bit too.
It may not look pretty, but it tasted damn good for a first try. Mind you, both cheese's are homemade, so the melt is not necessarily the best representative of this method. It's better than any oven/broiler/steel method I've ever tried too. I bet with a decent heat gun, you could make a pretty killer Nearlypolitan like this. Definitely going to do this again.
Pic 1 - Second pie ~1.5 minutes on stone + a couple minutes with a heat gun on top
Pic 2 - Upskirt of 2nd pie
Pic 3 - First try ~2 minutes on stone (overdone) + heat gun
Pic 4 - Upskirt of first try
Pic 5 - Stone on top of 3 burners, middle burner has flame tamer removed.
Pic 6 - Aluminum foil drape to help insulate the stone while heating