Like many others here I have also been working on various methods to cook pizza at high-temp, for me in my BBQ grill. I recently had my best results so far, so I thought I would briefly describe the method.
Background: up to now I have had intermittent results; the two major problems have been uneven heating and too-long time to warm up the stone. I have been using a pizza stone on the grates with various things underneath it (bricks, plates, alu foil, etc) and above it.
The "new method": since I felt like I was not getting enough heat I decided to lower the stone closer to the heating elements -- I removed the grill grates and put the stone right over the heat radiator things (the pieces of metal right over the heating elements on my grill). Every grill is made differently so I am not sure how this method will work on different grills; the basic idea is to get the stone below the grate, yet not getting directly licked by the flame. I had to make some little supports for the corners to keep the stone completely level.
I coated the stone bottom with aluminum foil. I then heated it up until my IR thermometer read about 600F on the stone surface. Since I had the whole bottom coated with alu foil it took longer than when I had the stone on the grates, but still it took "only" 15-20 minutes to warm up which was a lot less than it was taking when I had the stone high up. At this point I baked some pies. They took 2-3 minutes to bake, and had the telltale spots of charring on the bottom, plus the big bubbles and browning splotches on top -- in short, it worked great. The first pie got burnt a bit on the backside bottom (not out of line compared to some shots I have seen posted here of genuine Napoli pies); for the next one I rotated 90 degrees after one minute and avoided that.
I am going to experiment more with this method. The one downside is it is a bit harder to get the pies in and out since the stone is below the lip on the front of the grill; otherwise all I am seeing is upside.
There ya go .. yet another method to try out!