My family (paternal line) was also in New York and in New Jersey, so I've used Italiangen and Germangenealogy a LOT.
When I hit one wall, I hired 2 pros to retrieve some documents in NYC and NJ archives which helped a LOT! I moved past that wall, at a reasonable cost. I live in Michigan and all the relatives who once lived in New Jersey or New York are now deceased or moved farther away.
I notice your frustration with the variation in country of origin. It might be helpful to study the instructions to census enumerators, if you have not already done so. I don't have the exact wording before me, but the enumerators (and those being questioned) were instructed to record the country as it was known in the census year. Some of my family members are variously recorded as having been born in Russian, Poland, Czechoslovakia, Prussia, etc. Same person, same place of birth, but the borders kept changing.
Census enumerators were human too - and made assumptions or were mis-informed, either accidentally or not. My paternal branch is primarily from Northern Ireland, before the division. Many of them are recorded as having been born in "Irish Free State" - which is absolutely incorrect, but an assumption. Plus the census enumerators that year had a rubber stamp for Irish Free State - too easy to mark it wrong.
The Library of Congress website has some excellent resources for New York newspapers - I've found a wealth of family info in newspapers there and on fultonhistory.com
Good luck and happy to help any way I can.