another alternative for this type connection is to just rent a one-way rental car (between the 3 NYC airports there's rarely a drop charge). This way you can secure the luggage while doing what might be interesting (obviously deep Manhattan probably isn't the thing do do, but there are interesting parts of Staten Island/Brooklyn/Queens which can be done to fill up a day between EWR and JFK. Have done this once upon arriving at EWR at about 8 am and leaving from JFK at 6 pm. Explored Staten Island, Crown Heights, and Howard Beach.