JFK (NY) Park Sleep and FLy

We are flying out of JFK and have a 6am flight. Looking for a package near JFK where you can stay in a hotel, park there and they shuttle you back and forth to the airport. I tried parksleepfly.com and they don't show JFK (only La Guardia & Newark). Has anybody done this that can help us.

This is what I found: http://www.parksleepflyhotels.com/jfk.htm
Another one is: jfkennedy.airportdeals.net/Hotels
I hope this helps.

Try the second link. The other one does not find hotels even though it shows JFK. Good luck!