Your reading of the NJ instructions is correct. Unfortunately I don't have the NJ or NY downloads on my computer (I'm a fellow user, not a TT employee), so I can't duplicate your situation.
The best I can do is again to refer you to this previous TT answer on this problem:
https://ttlc.intuit.com/community/state-taxes/discussion/can-i-file-both-a-resident-and-non-resident...
If that suggestion doesn't work, I suggestion posting your problem as a new question. Maybe a NJ-based user will pick up on it and be better able to help.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
