It is difficult to diagnose problems like yours from behind a keyboard, and especially so since you are also new to pizza making and experiencing the same kinds of problems that newbies experience at home. However, it is common for the Lehmann NY style dough to spread as it ferments due to relaxation of the gluten and the effects of enzymes in the dough on the gluten. Also, just because the dough spreads does not mean that it did not expand. I use the poppy seed trick for my doughs and I see that phenomenon all of the time.
It might help in your case if you describe in detail how you made the dough, from beginning to end, including the water temperature you used and the finished dough temperature when the dough came out of the bowl, I might spot something that needs correcting. The two factors that are most responsible for the degree of dough expansion and the window of usability of the dough are yeast quantity and dough temperature during fermentation. Dough temperature is a function of the flour temperature, room temperature, water temperature, frictional heat of your mixer, and the efficiency and temperature of your cooler/refrigerator. If the weather is still cool where you are and you are also using only one day of cold fermentation, it may be necessary or advisable to increase the amount of yeast. I assume you have not been re-kneading or re-working or re-balling the dough balls in preparation for using to make pizzas. If so, that could account for the problems you have been having opening up the dough balls to the desired size. If you have not been doing these kinds of things to the dough balls, it may be necessary or advisable to increase the hydration of the formulation a bit.
It is not unusual for a dough formulation to need modification to fit the circumstances. So, once I hear back from you, maybe I can offer up some suggestions.