I don't think that singapore aircraft are on the 'N' reg, but I'm failry sure they will accept an 'ICAO' licence, an FAA CPL/ATP is 'ICAO'. I guess they would issue you with whatever their licence is. For example I think that Cathay Pacific issue a Hong Kong ATPL on the basis that you have an ICAO licence and pass their Air law and performance exams.
In short, if it's not a European commercial operator then a good chance your FAA licence will be accepted. Also if you have an FAA first class medical certificate and a CPL then passing the JAR class one is treated more like a renewal. I know 2 pilots who failed the JAR class one, got an FAA CPL then tried the medical again with success. Not gauranteed but worth looking at.
I cant help you with information regarding being a national.
No doubt somebody will shoot me down and tell me it's crap...