Since the reality is that your income is legally not subject to NJ income tax, I would absolutely file a non-resident NJ return on which you show the NJ withholding but allocate zero income to NJ.
If NJ questions your return, you can explain the situation just like you did here. If NJ requests corroboration from your employer and your employer refuses, get their refusal in writing and show it to NJ.
An alternative would be to print and mail your NJ return, along with a written explanation of the discrepancy between your tax return and your W-2.
The facts are on your side.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
