The problem with your scenario is that you will never be eligible for NYS aid as your family must have a physical presence in NYS (living in NYS).
Right now you are talking about accumulating a minimum of $140k in dept for an NYU degree.
As a person who holds 2 degrees from NYU I can unequivocally tell you that unless you are attending NYU Med school (which now has free tuition for it’s incoming class), there is not a program at NYU that is worth 140k of debt. As a parent that I have been there done that as I told my own D that NYU law needed to come off of the table because if was not feasible to start her career with 6 figure debt.