i would also use the few hours to catch a little bit of singapore's nightlife. most of the bars close at 3:00am, but there are spots that stay open longer. taxis are not a problem at all after midnight, so you should be able to get one easily whenever you want to switch locations.
after 3:00am, you can still get drinks at mitre hotel behind orchard road (every taxi driver knows it) and watch the crowd. it's a bit shabby but famous for after-hours. or you can go and get something to eat at one of the many 24-hour hawker centres (Newton Circus or Lau Pa Sat). east coast park for sunset is nice, too.
if you really can't stay awake you can always book a hotel room for a few hours (i think the hotel 81 chain in geylang rents clean, standard rooms by the hour and is quite cheap). have fun!