Bad idea all around. The Van Wyck will be horrible. The Cross Island to the Belt? Even more horrible.
Have your friend get to the airport on his/her own and meet at the gate. Tell me where this person is starting and I (or one of us here) will get him/her to the E to the Airtrain or to Penn Station for the LIRR to the Airtrain.
I would get to JFK 2 hours early (you'll need time to return the car and hop on the Airtrain). You will sit in traffic tomorrow—it's bad enough that it's a Friday night. It's a pity you can't return the rental earlier and take public transportation to JFK. But I don't know if you'll be coming from Manhattan, one of the boroughs or one of the burbs.