Using today's cheeses, will I be able to cook this 'lil thin thing hot enough to get some "bite" out of the cheese without throwing everything else off kilter?
I am not sure what kinds of problems you have in mind but when I made cracker style pizzas, my preferred practice was to use a cutter pan (although I did try direct baking on a stone) and, after pre-baking the crust, I put the cheese (in slices or shredded or diced) directly on the crust and then followed with the sauce and toppings. Putting the cheese down first was an idea that I got from Tom Lehmann. I believe I saw the idea at http://www.pmq.com/Recipe-Bank/index.php/name/Chicago-Cracker-Style-Pizza-Crust/record/57734/
. I think putting the cheese down first helped keep the sauce and any liquids from wet toppings from migrating into the crust and reducing or impairing its crispiness. The cheeses were also protected from excessive browning or breaking down during the prolonged bake time following the dressing of the pizzas after the par-bake.
I don't know what sequence PH uses to assemble its pizzas and how it bakes them but I would imagine that the pizzas are baked on screens in conveyor ovens.