I don't have an answer for you. As you have noted, the problem is that the New Jersey tax forms make no provision for your situation. TurboTax can't provide a way to handle a situation that the state forms don't provide for.
I suggest that you call or email the NJ Division of Taxation and ask them what you should do. Post a reply in this thread to let us know what they say.
Phone: 609-292-6400
Email contact:
https://www.state.nj.us/treasury/assets/contact/taxation/contact-taxation.shtml
