I've got even worse news for the OP. By my cursory review of the schedules, there are no nine hour same-day connections at JFK on a DFW-JFK-BDA trip. It looks like the OP arrives at JFK about 10:30 pm and then departs for BDA the next morning. That means the OP is gonna have to spend the night someplace outside security, and certainly not at an Admirals Club. They don't stay open all night. The new terminal is certainly nicer than the old terminal for all-night connections, but still not ideal.