To get that NY "elite" style of the Lombardi's pie, I think I would look locally in a good Italian foods store that sells a fresh mozzarella. I would slice it thinly and drain it on paper towels to get some of the moisture out. Where you are, I think you should also be able to get some fresh versions of the Polly-O and Mozzarella Fresca fresh mozzarella cheeses, either in the supermarket or, for the Mozzarella Fresca, in a Whole Foods. Where I live (in Texas) the best I can do at reasonable cost is the Mozzarella Fresca and the BelGioioso fresh mozzarellas. I slice and drain these cheeses also or use them in large pieces so that they don't cook too quickly. Otherwise, they can break down and look like ricotta. Since several of our members have had problems recently with some of the fresh cheeses at Trader Joe's, I would pass on them for now even though your local TJ's may be perfectly fine.
PennMac is a very good source of pizza ingredients in general. You can check out their website at pennmac.com (look under the Pizza Makers tab), but they sell a lot more items than are listed at the website. If you want to try the All Trumps to mimic the Lombardi's dough, PennMac sells the All Trumps in 5-lb. bags. I have tried the LaValle San Marzano and, while I don't think they are as good as the DOP LaValle's, which I don't think PennMac stocks, they are still good and should be comparable to what Lombardi's uses. Our resident canned tomatoes guru, scott r, is a fan of the LaBella tomatoes, even though they may not be the authentic San Marzano varietal (despite what the label says). Shipping charges for these items are unavoidable but it will perhaps be cheaper than driving from Philadelphia to Pittsburgh and back.
If you chose to go with the Lehmann dough formulation, you can omit the oil if you want to get closer to the Lombardi's dough formulation. I don't recall how thick the Lombardi's crust was but it easy enough to modify the Lehmann dough formulation to make it thicker or thinner. Maybe one of our members who has eaten enough Lombardi pies and Lehmann pies can compare the two crust thicknesses.
To use the Lehmann dough to make a more "NY street" style, I would go with the Escalon 6-in-1s or a comparable Stanislaus canned tomato, and I would personally go with the Grande mozzarella cheeses, or maybe a Polly-O mozzarella. If you are into pepperoni, Ezzo would be a good choice. All of these products (I'm not sure about the Polly-O) are available at PennMac. For hard cheeses, PennMac also carries both the Pecorino and Locatelli Romanos, although you should be able to get either of these locally. If in doubt about anything, call Rose at PennMac. She is a member of the forum and deals with our members all the time.