BUT...all was not lost. A young Singaporean guy contacted me via Facebook, to let me know that his mother had found my phone and was holding onto it for me. Apparently they found the phone, which was all out of batteries. They bought a new charger, charged the phone enough to turn it on, found my name on the phone, used the name to search Facebook, and sent me a private message once they recognized my picture (as there are a lot of people with my fairly common name on Facebook; luckily my phone has a background photo of me with little R). Wow.
I went to their apartment (out in Jurong West for those familiar with Singapore geography, which is a relatively poor neighborhood) and picked up the phone, just as good as new.
I am so grateful to them for taking all that trouble. It was truly kind (especially for a stranger who they'd never met!). I mailed them a thank you card and Starbucks gift card (since I had their address from picking up the phone), but honestly there is no good way to repay them. What nice people.
They were exceptionally kind, but their honesty and concern to do the right thing are very typical in Singapore. Violent crime is almost non-existent here, but petty theft and other types of property crimes are also very rare (especially among local Singaporeans; the theft that occurs tends to be committed by immigrants from elsewhere). Singaporeans may be a little bit rigid, but they definitely have a high standard of morality (to my great benefit). I can't imagine this story occurring in the United States (and as for China, the very idea is completely ridiculous).