Why not change the flight out but leave your return as is? There's no law requiring you fly in and out of the same airport. You can likely Uber to the airport and take some sort of transport van home from JFK on your return. If you need to drive yourself to the airport, you can also rent a car on your return and drive to the other airport, returning the car there. Most rental car companies consider all the NYC airports the same (no one-way drop off fee), even Newburgh.

I often fly in and out of different airport when in NYC. Even in other places, I fly into one city and return to another, like into Buffalo, spend a day there, drive to Syracuse, spend a day there, and leave from their airport.