Been reading this post for quite abit. Would like to relay some opinion on this matter.
Like many on this board, I graduated from an engineering degree ; electrical engineering to be precise in 2009. Market was horrendously bad then. Only jobs up were the LOT programmes and government-related ones. I took the option to capitalise on the (bad) market conditions and slacked for close to 1 year before finding a job.

I knew engineering wasnt my cup of tea, hence I was lucky to get a junior back office role in an international bank, paying me 3k. The job there was really boring and I held it out for close to 1 year. Fortunately, due to some restructuring, I was moved to a business analyst role in a business integration team. Paywise increased by 15% ( inclusive annual increment ). I did that role for about 10 months before managing a change to an investment management firm doing financial pc/risk-reporting control role, drawing about 4.7k now.

So, I guess its not impossible for engineering-educated people to venture out and test the external markets. Just keep on trying and constantly look for openings. All the best!