I don't think you can pay to use the Club America lounge at MIA, although it is open to Priority Pass members. Failing that in the past I've found the restaurant at the top of the airport hotel to be a decent place to spend some time ... great views ... as long as you get back through security in time for the flight.
There's a plane at JFK, to fly you back from far away
all those dark and frantic transatlantic miles