This is really tight and possibly not doable depending on the carrier on which you are departing (and its check-in requirements). Other factors include: checked luggage? Check-in required at JFK? Pre-Check?
My recommendation is to book a car service so that you know that you have a car and don't have to waste any time at all. Don't have the driver meet you at baggage claim, but have him ready to pull in ASAP as you walk out (hopefully without checked luggage).
I take it that you have looked at the relative costs of routings which include a transfer at JFK or even LGA?