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A rental car will add up once you account for the tolls and filling the car back up with gas.
Also, the Belt Parkway could make that trip hours long even at 11pm.
Could always take the AirTrain to Jamaica, then LIRR to Penn Station NY, and then NJ Transit to Penn Station Newark.
A simple option would be to see if you could change the train to depart from Penn Station NY.
Can also see if the airline would let you change to EWR too.