i'm in taiwan now.. staying at the Jiangzicui MRT station area. which is close to the Banqiao district.. stumbled upon a DBS bank as i was wandering around the area. Outside the bank theres a notice that says Foreign Currency Exchange.. so i guess you can change your SGD there?
Exit from Jiangzicui station Exit no.2, walk straight out from the exit, you will pass by HSBC bank.. walk straight on and you will see a Family Mart.. (sometimes theres a young school girl working there as a cashier. hehe) walk straight on and to your right you shld see a DBS bank...
hope this helps too!