This time of year, with warmer weather upon us, you may want to reduce the amount of yeast a bit, use cold water right out of the refrigerator or slightly warmer, and put the finished dough in a metal storage container with a lid to go into the refrigerator. That should help prolong the period of fermentation.
Normally, with a dough formulation such as the one you have been using, with only flour, water, yeast and salt, you should be able to get a reasonably firm slice in the 12" size pizza. Most NY slices have a small amount of droop, especially when the pizza comes out of the oven and hasn't had much time to cool. It's possible in your case that the Varasano method you have been using is creating a more tender and soft crust and crumb. Maybe the next dough without using that method will tell you whether the method is denying you the crispy and firm slice you are after. You might also consider a longer bake at a lower temperature to dry out the crust a bit more and make the crust firmer. With the thinness of your pizza, you also don't want to overload it with sauce (or use a dryer sauce), cheese or toppings. Another possibility is to pre-bake the crust before dressing it and finishing the bake.