Sleeping in AA Terminal 8 at JFK

I’m looking for suggestions. I have a 10 hour layover at JFK where I get in about 7pm then have a red eye at 5:30am.
The Admirals club closes at 11:30pm and won’t reopen until 4:30 am. Who closes their executive club?

Anyhow I’m looking for suggestion on where to catch a few Zzzz’s while waiting. It’s not enough time to check into a hotel.

Thanks

Every US carrier closes their club from the time the last flight leaves until 2 hours before the first flight. There’s a 24 hour cafe in Terminal 4.