In the worst/best case scenario, you could book a room at the transit hotel and store your luggage there.
http://airport-hotel.com.sg/
I have checked into the transit hotel and then cleared immigrations. Make sure you have your onwards boarding pass, though, as you'll need it to reenter the airside area.
[Further note after looking at the hotel's website]
The site does say "Please do not clear Immigration/Customs" - I don't know whether that means you're not allowed to, or that it may otherwise be confusing because you'd need to come back in.
Greg
[This message has been edited by greg99 (edited 01-20-2002).]