Are you using sliced cheese for deep dish or shredded? Shredded usually has some powdery agent in it to keep it from sticking, which can hinder proper melting. Besides, DD calls for sliced cheese.
Cornmeal has no place in pizza dough. Corn oil, yes. Cornmeal, no. I mean, you can put whatever you want in dough--but that ain't authentic.
I like Cooks Illustrated for many things, but this recipe isn't one of them. It's too fussy, has too many procedures, and is just plain goofy. It doesn't surprise me that it makes an edible pie, but you can do a lot better and a lot easier with just about any of the recipes on this forum.