I believe car rental companies at JFK are open 24/7, so that should be fine then. I could also have my relatives fly to EWR but I'm guessing it makes no difference.
One oddity about Avis is that they don't seem to time-stamp rentals based on when you pull out. Just when they print the contract or you select the car in the app.
That's interesting. I thought all car rental companies recorded the time when the contract was signed, not when the car got out of their parking lot.