I've done exactly what you're speaking of two weeks ago in Hong Kong. I can't speak for Singapore of course, but it was quite easy in HKG. I considered going thru SIN, especially since the Saturday office hours at the AA office sync'd with my schedule a bit more. In the end, I decided on HKG, since I wanted to use my 26k miles in North America, rather then getting in & out of Singapore.

The DCIR26 reservations were setup and priced through the AA RTW Desk in the US (+1 800 247 3247), who I'm quite loyal to. Then, on a stopover from the US, stopped in to the AA HKG office, and had 2 DCIR26 tickets issued 10 minutes later.

I live in Australia, and my credit card was issued in the States, but the ticketing staff didn't ask. 8 hours later I on a plane to Australia.