Your DL D1 boarding pass will not get you into any lounge, even with a SC membership, Reserve card, or regular AmEx Plat or Centurion card. IIRC DL still uses SkyView in T1 for D1 departures. It is open all night and should accept PP. There may be other PP lounges open all night too, although I know the swimming pool closes at about 11 pm.

I'd suggest one of the airside transit hotels. You need to make a reservation in advance via their website, although IIRC it doesn't directly show availability. IME you get an email confirmation in about 24 hours.