Imo, if you are good at what u been doing in ur current role, and they need ur specific skillsets n experience, you shouldn't ask less than what u getting now , in SGD

Compare dollar to dollar is like compare orange to apple.
A friend of mine, he got SGD8k from a shipping company while he's earning RM12k. I got SGD2.8k while I'm earning RM4.2k. Did you see the ratio?
SG is going into deflation nowadays, the food is cheap, a meal only costs u about SGD3.00 in the hawker centre. But the working environment is stressful, especially for tech support, end users in Sg are more articulate and computer savvy. Good and bad, it depends on how important you perceive money.
By the way, do you mind to share with me what role are u doing? Software dev, tech support, or consult?

Software house tends to be more appreciating their staffs. The only difficulty is handle end user, stress management is quite important for consultant. Perhaps u can do some survey into the company environment, whether it's very politic or management problem, that's important to u. all the best

I was drawing $5.5k with 3-4 years experience as a BI developer in a foreign bank, never OT everyday yumcha 3 times.

You really should just look for other companies, 6k for BI lead is waaaaay too low.