Maybe you should call customer service, and have them issue you a hotel voucher (or visa sponsorship is called) for pick up at check-in at JFK.

This is what I usually do; sometimes I even forget about it, and they chase me up into the lounge, or onboard right before departure.

The standard is if you're in Y and have a minimum of 8 hours up to 24 hours connection time, you get to stay in the airport millenium hotel ek wing which is a min ride by bus (provided). But they have issued me that even when I had 6 hours or so.

In F/J you get the Meridien with the chauffeur drive with a minimum of 6 hours connection time.

dusordua: I think it depends on the booking itself, not on whether there are earlier flights.

If you want to avoid the long stop over try changing to an earlier flight ex-DXB, they have at least 5 or so a day.

Cheers