Josh, that's a pretty nice pie for someone with 'several weeks' experience. Something tells me that you're attacking this new hobby with a vengeance
I'm also impressed at how quickly you've acquired tools that most beginners tend to be hesitant to purchase, namely an IR thermometer and a digital scale. Well done.
While I applaud your desire to produce a traditional 16" pie, I think your workaround to achieve that diameter might be a bit counterproductive. Screens are notorious for insulating the dough and extending bake times and that's using them on a stone. Using them on a rack, imo, is the kiss of death for oven spring, even on the lowest rack with a red hot bottom element. If you absolutely have to use a screen, put it on the stone straight away, and then, once the bottom is set, make the transfer from the screen to the stone. Ideally, though, you'll want to remove the screen from the equation.
I know you just bought the new stone and the last thing you're going to want to hear is that it's not big enough, but if you truly want that coveted 16" diameter with the classic puffy chewy NY style crust, you've got to get a bigger stone and nix the screen. The good news is that, with your frozen towel expertise/willingness to push your oven to higher temps, you have some options when it comes to stones. If your oven can fit it, I'd go right out and get an 18" x 18" x 1" cordierite kiln shelf. If that's too large, get a 17" x 17" x 1" one. Both will put out a 4 minute bake time @600 with a peel delivered pie. The nice thing about that 600 degree stone temp is that you'll be able to use the broiler during the bake time and not exceed that critical 700 temp.
You could, in theory, pick up some less conductive, cheap quarry tiles, but that's going to require closer to 650, and, imo, with broiling, put you too close to the turn off temp. Having the machine shut down during one pie might not be the end of the world, but if you've got a second pizza to make, that's going to be a problem.
Re; windowpaning. Windowpaning is suitable for same day/unrefrigerated doughs, but it's too much kneading for anything that's cold fermented. I'm not all that familiar with your flour, so I can't say for certain how long to knead it, but I'm relatively certain that you're going to want to dial the kneading back for ideal extensibility.
As far as the thinning in the middle goes, that's something dough has a tendency to want to do and that you have to actively work against. Here's a good video on forming (ignore the rolling pin stuff):
Lastly, it's always a good idea, especially since you're using the dough calculator, to copy and paste your recipe here.