I've done the overnight before a SQ flight with TPR visits for dinner and breakfast, spending the night in the transit hotel rather than getting up early in a downtown Singapore hotel before my flight. However, the problem is that you cannot do this with a USA legacy carrier nonstop flight to the USA as you must answer security questions at the airport before being permitted to go airside, and this can be done only after your USA carrier opens their check in desks in the (early) morning of the day fo departure.

OTOH, if you're connecting from elsewhere, even on separate tickets, you can simply remain airside and visit the transit hotel, lounges, swimming pool, movie theater or whatever during the evening (or more) before your flight. In this case, at worst you get the exSIN boarding pass at a transit desk and answer security questions in the gate area before boarding (allow a couple extra minutes at the gate for boarding in this case). If you have a bag checked to (only) SIN, either the transit desk will call and have it retagged or you can go landside at your convenience to retrieve the bag and recheck it when your USA airline opens its check in desks several hours before departure.