Is there any lounge open at that hour that will let me in with an UA arrival business boarding card?
You "might" get lucky at the SKL in T2. It is NOT a *G lounge, but does accept UA C class BP's for entrance. The problem of course will be how they look at the "same-day" travel in C issue.
If they aren't too crowded (which I can't imagine!) - you could get a nice Matron who will concede that you're travelling same day on the inbound.
OTOH: you might not.
Good luck, Dave