[jyl]

I would do this
- Put bricks in the lower part of the Weber, leave just enough room for the coals (edit: oops I guess you have one of them there girly pro pane grills - anyway, same idea)
- Put the pizza stone on top of the grate, so the pizza slides onto it
- Stack bricks on the grate, around the stone, fill up as much of the volume under the lid as possible
- Get it to 700F and keep it there, so that not just the air is 700F, but all that brick and stone (60 lbs?) gets to 700F

Now, you open the lid and lose all the hot air. Or a little of it, if your fancy sneaky peel idea works. But the point is, the hot brick and stone stays.

Compute mass x specific heat of a couple cubic feet of air vs mass x specific heat of 60 lb of stone. You can see, you've lost only a tiny fraction of the stored heat in the Weber.

Plus, the 700F pizza stone will transmit heat to the pizza far more effectively than will 700F of air.

The only bummer will be if the Weber's legs collapse under the weight.