Could I use any JFK lounges while waiting for a JFK -> POP flight (POP is Puerto Plata, Dominican Republic)? I am in business class, arriving JFK at 6:15 AM and departing around 10:30. I'll be coming from SFO and it will be early, so a comfy, quiet place to doze is really all I'm after.

The lounge policy linked above seems to indicate I would not be able to enter the Admirals Club, since Caribbean destinations are not considered international (!) Is that correct? If so, has anyone had any luck getting exceptions? We paid extra for business class in the hopes of having a comfortable journey, and 4 hours at the gate starting at 3:15 AM west coast time does not qualify.

Thanks.

Edit: I have no status on AA or any oneworld partner. I'm Star Alliance Gold (UA 1P), but somehow I don't think that will help.