My concern is that I will file the New Jersey return and pay taxes on the money I earned while working and living there, and file the New York return and ask for my money back since I don’t live or work there, and if New York denies the refund, I’ll be paying taxes in both states.

It’s unclear at this point whether New Jersey will let New York claim all this taxable income or whether New Jersey will try to claim it for itself (it needs the money too). The tax rates are pretty similar in both states but my preference would be for the money to go to the state I actually live in.