Very similar itinerary for me couple of weeks ago, I did the 183 to JFK and had a flight at 0700 next morning to BGI, the 183 was late arriving due to a wheel change at LHR which helped a little, zero queue at immigration so was landslide at T8 around 0000, I just sat opposite the Hudson news 24 hour shop on the air train level, there’s some big metal window leges which were ok to sit on, the 24 hour pop music was ok and there’s free terminal Wi-Fi, you can also pick up the Wi-Fi for the soho lounge (password is Brisbane) security opened up around 0315 and I sat at a gate near the soho lounge until it opened, first in the soho, straight in the shower and had breakfast with the lounge just about all to myself, it was an ok experience and in my opinion was better than forking out for a hotel for the few hours I was there. Nice surprise was JFK-BGI was 2093 miles so got 140 tp’s rather than the 40. I thought I’d get.