On this one, I flipped it over and pulled the ingredients in, then flipped over the other side just over the top. Something I had picked up from Emeril. I used a bit of egg on top, with some coarse sea salt. It's a good idea to put some slices along the top to let some air out to avoid burst when it's wrapped like this. I put a buffalo mozz down first, then some thin slices of dried tomatoes & fresh herbs, along with a bit of olive oil/red wine vinegar, some salami or pepperoni or prociutto (can't remember on this one), and a touch of yellow mustard.
I used 2 cups of flour, which was a combination of Gold Medal Specialty Bread flour (12.7% protein) and King Arthur All Purpose (11.7% protein), and added some herbs into the dough. I left the dough in the refrigerator for a couple of days to get the taste I prefer. Waited an hour at room temp before stretching it like you did. I think I cooked it at 470 F for about 13 or so minutes in the middle of the oven.
Once it was done, I waited a few minutes, then sliced it down the sides to make plenty of appetizers-- the crust was crispy on top, but airy and tender inside,and it held together fairly well. I've tried it with less of an overlap, and that works okay.