Private schools offering overseas degree courses from unmarketable universities are designed to offer foreign students an excuse to stay in Singapore. They are not meant for locally bred Singapore citizens, who should stick to SMU (ranked 585), SUTD (ranked 440), SUSS (ranked 3,532) if they cannot get into NUS and NTU.
In the worst case scenario, go to the local polytechnics. I especially recommend NP. Although NP has yet to produce a Nobel Prize winner, it has nurtured a 赌神.