I love the original thinking here. I believe what you are suggesting is a “T” shaped design (looking from the side) where the upper line making up the T is the pizza stone and the vertical line is the tile. If so, maybe it looks like TTTTTTT imagine - assuming all the upper lines are the continuous pizza stone – when viewed from the side. If that’s what you are suggesting, then read on.
I like the idea for the following reason. That SP10 can put out a massive amount of heat, much of which blows out the upper vent. I don’t know the warm-up time in your configuration, but assuming it takes 30+ minutes for the stone to reach steady-state, uniform cooking temperature, then those vertical tiles will be hot as well, and could provide residual heat keeping the pizza stone warm. IMO, there is going to be a big performance difference between having the tiles touching the pizza stone and leaving a slight air gap. My sense is that the gap is a better idea so you don’t get hot spots.
But here is where I think the problem is. You only have one source of heat with enough air flow to cook the upper part of the pizza, and that is the SP10 burner. Turn that off, and even though the cooking surface stays hot, the top of the pie won’t cook much at all. The SP10 is such a blast-furnace, that most LBEs try to insulate between the direct heat and the stone and vent the heat over the pie.