D.C. Pizza Master,
I live in Texas and only get to NYC once in a while, so I will never be an "expert" on NY style pizza. But a lot of the members on this forum, especially those who grew up in the city, have taught me a fair amount about the NY style pizza.
Most of what you have said about the NY style pizza is correct. Most of the NY style pizzas are around 16-18 inches in diameter. Once in a while a pizza operator will want to show off and make a pizza over 20 inches, but that is not common. The crust of the NY style pizza is thin, a bit leathery and chewy. The rim (il cornicione) can be small or large, but I am told that the rim is more often small rather than large. When a NY style pizza is cut into slices, the tip will droop when you hold a slice by the rim. The slice can be folded in half, usually lengthwise, but I understand that some fold the slice from tip to rim. I believe the Italians would refer to these techniques as a libretto or portafoglio.
The NY style pizza most often uses high-gluten flour (around 14% protein), which contributes to the texture of the crust and, to a degree, to its color. A high-gluten crust will also lend itself better to holding a lot of toppings, which is much more common in the U.S. than in Italy, from what I can tell.
Most skilled American pizzaioli seem to be able to expand the dough into a fairly large disk without much difficulty, using their knuckles and spinning and tossing to do so. Your technique reminds me of the way that phyllo dough and strudel dough used to be made-entirely on a table, by stretching and pulling the dough outwardly gradually, drooping it over the edges of the table, all without much lifting. That's become a lost art.
I hope this gives you a better idea of the NY style. If I have left anything important out, my colleagues at the forum will set me straight.