I was just reading your post and although I have no real info for you the best I can tell you is to try Malaysia. Any records before Singapore became independent will be with Malaysia (not sure if link can be of help..but http://www.jpn.gov.my/en/servicesmarriageordivorce
...its worth a try. Your main problem is with the government not keeping great records and they are usually too lazy to bother to try and look . I know from experience as my husband is Singaporean and I gave birth in Malaysia. Good luck!