Thanks for all the advice and information, everyone. I've been doing a bit of research today and the transfer hotels definitely seem like tenable (and cheap) options. On the other hand, there also appears to be a reasonable amount of stuff to do in Singapore in the middle of the night.

I'm torn between 1) staying in the airport for my entire layover (not very exciting, but probably pleasent enough) and 2) doing a bit of exploring between 12 and 6 (more adventurous, but perhaps a little draining).

What would you do? Do any of you have any experiences with jet lag on day flights from the US to SIN? What's Singapore like in the middle of the night? Are there any differences between the terminal 1 and terminal 2 transit hotels?