Besides JFK, I would also look into LAX-EWR and LAX-XXX-LGA. Might need to get creative with connecting somewhere in between or going to an airport on the east coast like BOS, PHL, DCA, IAD, etc and nonrevving from there or taking ground transportation. As others have mentioned, that is the busiest time of year for travel in the US. Might be ok Fri and Sat. Many employees end up buying tickets on their own airline. Try for the first flight of the day and hope for people who oversleep.

As you probably know, the powers that be terminated the ZED agreement between EK & AA.

Good luck!