Not sure if this will work out. Both Priority Pass and the website for the lounge operator say visits are limited to 3 hours.
Further, while PP says the lounge is open 24 hours a day, the lounge operator says it closes at 11 pm or 12 am depending on day of week.
It would be quite unusual for a lounge in the US to be open all night.
I booked a reservation for it at 1 am. 3 hours is enough for me. I'll swing to breakfast at a lounge and then get on the 1st flight out.