PapaJon, although the burned bottom is a bit of a bummer, you definitely have a lot to celebrate. That's great that you were able to obtain an IR thermometer. I'm also very impressed with your oven spring/crumb. All that's left is evening out the top heat with the bottom.
I wouldn't mess with aluminum foil nor would I utilize the broiler compartment. Aluminum melts around 1100 f, and although you probably won't hit that in your oven, it is hottest close to the broiler and I wouldn't take the chance, especially since, if you've got the right setup, you shouldn't need to.
I'm pretty sure your answer will be an oven within an oven. Leave the cordierite where it is, and, on the shelf above it, lay down quarry tiles, a large pan or the second stone surrounded by foil. Here's a few things to keep in mind:
1. Isolate the bottom of the oven by covering as much of the shelf as possible, so the heat coming up from the bottom burner collects on your makeshift ceiling, rather than leaking to the top of the oven.
2. Thermal mass will probably help, but it may not be critical. If you can cover the entire shelf with quarry tiles, that's good, but you might be able to get away with just foil. As far as the materials go, conductivity doesn't make a big difference when it comes to radiation, so poorly conductive materials like quarry tiles or firebrick splits will work fine.
3. The darker the ceiling, the better. If you go with quarry tiles or firebrick splits, try to get dark ones, as they'll radiate heat better.
4. Proximity of the ceiling to the pie is critical. The closer the ceiling, the better the top of the pizza will brown. 4-5" should probably do it. It might be a little cramped when working with a peel, but it has to be that close for the radiant energy emanating from the ceiling to have enough impact.
That's how to correct your top heat issue. As far as the cordierite hearth goes... although the Raquel recipe has evolved over the years, I think your best bet is to shoot for a Neo-NY bake time. With cordierite... I'm thinking 625 might be just about right for a 3-4 minute bake time
Summing up, build a relatively air tight ceiling 4" above your cordierite hearth, preheat the hearth to 625, and, while the pizza is baking, have the gas flame going at full blast, so the heat collects in your manufactured headspace and bounces back on the pie.