Sounds like you have done quite a bit a searching already. In genealogy
there is the idea of a "FAN club" when you have a brick wall: Friends
(Family), Associates & Neighbors.
If you are not familiar with the concept, there is an excellent online
article by Elizabeth Shown Mills entitled: "QuickLesson 11: Identity
Problems & the FAN Principle"
Did your immigrant ancestor have siblings? Have you checked records for
those people. Have you looked up where the people living next to your
immigrant ancestor were from, based on census detail? What about where
those in the cemetery section were from? What was his profession ? Then
perhaps consult NYC directories to see if he worked with anyone and see
where they are from. It sounds like you have experience, so I am sure
you can expand on the application of the FAN Club for your research question.
Good luck with your exhaustive (and exhausting) search.