You have made a ton of progress from when you first started. Congratulations! If you really want to emulate the New York pizza from your childhood I would suggest reading Jeff Varasano's pizza recipe website( I cannot post links so just Google it, it should be one of the first hits). He too was a NY local transplanted out of state to where the pizza was less than stellar. It contains a lot of good information and is a must read for anyone looking to get serious about their pizza.
While I believe he is right about the high heat, there are ways around it. Most of the pizzas you remember were baked in a deck oven running at about 500-550 degrees. Not all great NY style pizza is baked in a coal or wood fired oven, so with a little oil in the dough, you can create a well browned delicious crust. You have already made quite a bit of progress in that, so play with the amount of oil until you feel you hit it just right.
In terms of sauce, if you are still looking to improve that, when making NY style for my oven at 550 degrees, I use a slightly cooked sauce. I pulse the tomatoes in my food processor, add a little bit of oregano, garlic powder, olive oil, and red pepper flakes and cook it until boils. I prefer the garlic powder because fresh spices and aromatics tend to give a more marinara style sauce in my opinion.
Other than that, another good source of info is PFTaylor's Raquel Thread on this forum. That also contains tons of good information.