Hey,
I was born in Singapore, my father was a training captain and then a line captain with SQ for over 23 years but since I held a foreign passport SQ denied me time and time again but I can't blame them as they have had problems with foreigners leaving them for the Sandpit once they had some time and a type.
The thing I found was that Singapore, as you said is very limiting unless you get on as a Cadet. I was fortunate enough to be able to live and work in a few other countries. I did everything short of stealing to build hours and am currently an FO on the Dash-8 in the Caribbean. It's definately not SQ but it's a job and I still enjoy going to work.
Goodluck.
P.S as always in Aviation, it's not what you know but who you know. So get out there, shake some hands, exchange email addresses and keep in touch. You never know who's going to be sitting on the other end of the table in the interview room!