I'm puzzled by how you were able to incorporate 1 1/4 cups of water into 2 1/2 cups of flour. Unless you are using a heavy hand with the flour or a light hand with the water, or you are using a lot of bench flour, I estimate that the hydration is around 80%. I couldn't get any closer, even using my spreadsheet, since you didn't indicate what size pizzas you were making with the roughly 11 ounce dough balls.
The reason I ask is because recently, just for fun, I tried to make a Lehmann NY style dough with a hydration of over 75%. I was using a scale so I knew what the weights were for the flour and the water. By adding the flour gradually at low machine speed, I was able to get all of the flour into the water. I also used an autolyse. However, when time came to use the dough, after a period of refrigeration, it was impossible to handle the dough or get it onto a dusted peel. The dough stuck to my fingers all over the place. Once I was able to get my fingers out of the dough, I tried shaping the dough on a sheet of parchment paper (to which it stuck), and I then tried stretching the dough out between two sheets of plastic wrap (the dough just oozed and stuck to the plastic wrap). I finally pressed and shaped the dough in a cutter pan. Needless to say, the results were not what I was hoping for, although the pizza tasted OK. And, oddly enough, the oven spring was lot less than I expected. I concluded that it was not possible to make a pizza dough with such high hydration. It might be possible to make a ciabatta bread at such high hydration levels but not a pizza.