How can I apply for a NON-O Visa in Singapore with a US passport?

Seeing as you apply online for ALL thai visas at the Singapore consulate, email them. They're usually pretty good about answering back

OR

just make a user name and apply for it via their online system. They'll tell you what documentation is required AND they'll tell you when/if it's approved so you can fly down and turn in your documentation to get the visa too.