i wanted to say you can try to buy SPU degree and apply for
IDA. They have no right to reject it now since they publicly admit it's a proper uni. In fact, the whole Civil Service and stat boards should have similar standards and accept SPU degree now.
But i will give you proper advise. Yes, there's a difference in perception of degrees. SIM or private unis are below the local unis. But so are the local unis considered lower than ivy league ones. But qualifications only help you so far in the 1st couple of steps in your career. Later on it's about what you do with your career and how you build it up. I believe in getting a degree even though it's now so common but it still separates the normal staff and the supposed higher potential staff. The difference in a masters and a bachelor is less perceptible, so just aim for a bachelor's degree.
If i were you, i would focus hard on working well. See whether you can grow internally in your company. Move to a bigger company and work smart. Save up money and study part time or if you can afford it, quit and study full time in a local uni like
NUS/
NTU/
SMU/SUTD/SIT. If you choose to still hone your skills in the engineering sector, focus on getting a degree in
NUS or
NTU.