I've never built a pizza on the mat. Usually, she builds them on the wooden peel or a plastic cutting board while I make another crust. This looks like a good technique and I will certainly try it, but it won't work as easily if you continue to build your pie on the mat because you have to flip it over. A couple of things I've learned, though...when you open the dough ball, you want the top to be the bottom of your crust. The top of the dough ball is usually drier and firmer than the bottom. The bottom of the dough ball is usually somewhat soggy and soft, especially with higher hydration recipes, so you want that to be the top. I also spray/brush olive oil on the crust before she sauces it...it tastes good, it helps prevent the "gumline" (the layer of uncooked dough between the crust and the sauce), it adds color to the crust when baked, and it also helps to keep the sauce from penetrating into the dough. Good luck, Joe, and nice recovery on your stromboli!
EDIT: Also, I prefer rice flour over semolina or corn meal on the peel. It just seems to work better for me. Actually, equal parts of dough flour, semolina, and rice flour might cover all your bases. You can do a search on "Dustinator" at pizzamaking.com for the formula that Papa John's uses, too.