I do have one other problem (and that applies both to overnight lounge use as well as the transit hotel), and that is that of the checked luggage. It is not possible to check my luggage through (to the flight that I am connecting to). Which means collecting the luggage unless I let it sit around in lost and found till the morning. But then I won't be able to check in for my onward flight till the morning and won't be able to get back in to be able to use the transit area or a lounge (even a paid one). I am not even sure if Changi has any areas to hangout if one is not on the airside. I am trying to see if I can eliminate checked luggage somehow but it may be difficult.
I'm pretty sure that just about everything is airside in SIN. I would try to get a boarding pass from the transit desk before you collect your luggage. That way, you can collect your bags and then still get back airside and store your bags at the left luggage counter if necessary.
Also, I think the SKL is not the only lounge open 24 hours. If you are willing to pay a little (pretty reasonable), you should be able to get into any of the "public" lounges.