Just curious, have you tried talking to whoever handles UA's luggage office at SIN? If the bag is checked-bag ready, they might be able to send it back for you as a rush bag (like what they do to forward a delayed bag). Don't count on it, but it may be worth a try.

Personally, I honestly wouldn't have a problem doing it all things considered (I'm sure SIN officials wouldn't keep a bag without some kind of inspection) and if there is a protocol where they were aware of my arrival, then that's all the better. Sadly, I have no immediate plans to visit SIN. If you cover my expenses (including hotel and missed time at work) I'd be happy to help out, but that would probably cost much more than the $400 to ship it