It's possible you could get access to the QF F lounge. Official policy is that oneworld connecting lounge access is granted if the long haul flight is in F and the connecting flight is under 5 hours (which SIN-HND is not) but it doesn't hurt to ask, although you are right it does close at 11pm (unless QF1 is delayed onwards to London).
The Marhaba lounge isn't worth a visit nor is the Plaza premium or Sats lounge.
As mentioned the QR J lounge (which isn't open to those with status only those flying J/F) is a good option with a la carte dining and open until 2:30am, detailed review from Milelion here:
[URL unfurl="true"]https://milelion.com/2022/11/15/review-qatar-airways-premium-lounge-singapore/[/URL]
My only comment is that the QR J lounge is tiny and as a result if it's busy or wait times for a shower are long, you might have more luck at the QF J lounge (open until 1am) after QF1 has departed for LHR around 11:30pm.
