Although I now live in Boston I grew up in Pittsburgh and have been to Vincent's many times. I have been on a mission to try as many pizzerias as I can around the US including all the famous places like Pepe's, Sally's, Grimaldi's, Totono's, Lombardi's, Una Pizza Napoletana, and many many more. Vincent's is absolutely right up there with all the greats in my book. The reason you are having trouble getting something of that quality is that you are comparing to a pizza that is in my opinion one of the top 5 in the United States. Anybody, with even the best commercial oven is going to have a damn hard time producing anything close to the quality of Vincent's.
Here are a few things I have heard about the pies that you might want to try.
Molasses in the dough. Just a little.
Long fermentation time for the dough possibly all at room temp, and probably not as individual dough balls, but in bulk.
A blend of provolone and mozzarella, mostly mozzarella. This is HIGH QUALITY cheese and truly amazing. I think it is the tastiest processed cheese I have found anywhere. I have tried at least 20 brands of cheese myself and nothing I can get my hands on comes close. If you feel like peeking in a dumpster for me to find out the brand I would be in heaven.
A 650 degree oven that is never cleaned.
And yes, I think the smoke from Vincent's madman pie making style absolutely flavors the pie! I am glad to hear he has trained his employees at the new locations to throw them together like he does.