I may be more science-trained than some on this forum, but real-world results trump science in my mind, especially when it comes to thermodynamics and heat transfer. I have not kept up with the latest EggHead results, and should, but I suggest you keep a closer eye on their progress over my ďscienceĒ.
In some ways, itís great that the HD foil is melting. The places of melt will tell you where the hot spots are, and give some insight into airflow. Iíd get one of those thin steel cookie sheets, or some extremely thin sheet steel, and put that under the stone. The melting point of steel is entirely different from aluminum, and although the steel might rust over time, it will serve as a test. If you are gamey, pick up one of those craigs-list discarded stainless grills, and cut off a section of stainless using tin snips. There are differences in stainless (303 vs. 304, etc.) but ignoring that, stainless should be a reliable barrier and comparable in purpose to HD foil.
What Iím suggesting is a static/non-moving air gap between the impinging flame an the stone. Air, even hot, is a great insulator. The small holes in the stone are enough as long as the stone isnít directly in the flame.
The stainless steel pan you bought is great, but Iím still a fan of first putting a thin metal sheet directly under the stone, and if that doesnít work, later try the bucket for lava rocks. I see the bucket approach as adding a lot of potentially unnecessary thermal mass to the system causing longer warm-up times and possibly unproductive airflow. If one layer of steel didnít keep the stone temp low enough, Iíd try two layers of steel, separated by either metal lath or sand pebbles Ė something to add a little air-gap insulation.
Most important, do what works for you. Feel free to ignore these suggestions. The quest is tasty pizza, after all.