Authentic NY style pizzas, of which the Lehmann NY style dough recipe is one representation, typically do not have large rims. In fact, they trend to be fairly small and flat. However, if you want a larger rim that results from increased oven spring, I was going to make the same suggestion that Don (Colonel_Klink) made, that is, use more yeast. At 0.50% IDY, you should be able to get two days of cold fermentation. I actually prefer three or more days of cold fermentation, but that is just me (some devotees of the NY style advocate just two days). If you want to go beyond two days of cold fermentation, you might want to use about 1% sugar in the dough to be sure that there is enough food for the increased amount of yeast and to contribute to final crust coloration.
You can also let the dough warm up at room temperature longer than usual so that the dough can expand more and become soft to the touch. Technically, a dough ball can be used to form a skin at a temperature of around 55 degrees F. However, I personally prefer a temperature closer to 70 degrees F. There are also those who have found that they can use the dough right out of the refrigerator. However, that does not work for everyone, and the result might be a lot of large bubbles in the finished crust. Some people actually like that although professionals usually don't because that can mean having to use bubble poppers to pierce the unwanted bubbles.
In forming the skins you will also want to be gentle and try to avoid handling the rim as much as possible. Ideally, you want to try to force the bubbles in the skin from the center of the dough to the rim and contribute to a generally larger rim.
Unless your oven (which I assume is electric) is not operating at the proper temperature, I do not think that it should take 8 minutes to bake a 12" pizza. In my electric oven, 6 minutes would be about right.