would there be a way of mounting a second pizza stone above the first so that the pizza is surrounded by heat? Sort of the radiant effect that a cob oven gives.
In theory, a good idea - you could use two firebricks to support the smaller stone. But practically speaking, not sure that would be worth it. If one were to do it, you'd have to use a smaller stone on top because of the shape of the Weber lid. In addition, the extra stone and 2 firebricks would require 3x more energy to heat up, so you'd burn through coals a LOT faster. As it is, that stone requires a LOT of heat to get it to temp, which means you need a LOT of coals, and they burn down very quickly. So imagine what would happen by adding two bricks and another stone. Then you have the resulting heat loss from opening the lid several times during the cook, which also is just one more factor contributing to your coals dying out VERY quickly.
This is why I abandoned using it as intended and built a FrankenWeber kettle. Way less hassle, time, money, and it's always 100% consistent. Plus, I can get stone temps up to 800 degrees, no problem.
So for using this stone for charcoal, the two mods I suggested using a donor lid will be the easiest solutions to get top/bottom evenly cooked. Also, the open vent on the lid also has an added benefit - if you make it big enough, you don't have to keep opening the lid to see how the pizza is cooking and you can also rotate the pie while it's cooking so there's no loss of heat.
I also highly recommend buying an infrared heat thermo for this or any stone one would use on the grill so you know you're in the right ballpark. You want a stone temp of at LEAST 550 degrees to get good crust.