Guess I didn't really answer your question ...
I'd suggest for you to talk to more companies and be upfront about your actual current compensation. Don't worry about it seeming too high, and don't be shy to ask for what you want. If you have a skillset that a company desperately needs, they can pay your price.
Typical software engineer salaries range from $3000 at entry level to $8000 for managers/architects (non-banks). I would guess foreign banks or financial services companies range from $4500 at entry level to $10000 for staff engineers/managers.
Packages at foreign companies are generally better than local ones. American companies here generally give you a fixed annual salary (i.e. no bonus, fixed 12 months). Other foreign companies seem to follow the local practice of giving a 13th month and 2-3 months bonus. So be mindful of the gross annual package in your negotiations.
PTO (aka days of annual leave) typically start from 12 days at the low end, with banks giving 21-24 days. American companies are competitive at 14-15 days. Unlike in the US, medical leave/sick days is separate (i.e. not part of your PTO, as long as you are certified unwell by a doctor) and companies generally allocate about 12-14 days for these as well, though i don't hear of people really enforcing this strictly.
Larger MNCs (multi-national corporations) have better health insurance/dental/vision benefits than most local companies, again in general. Some even cover your spouse and children. Local companies typically subsidize you $25 per visit to the doctor, $75-$100 for dental, annually.
If you are a permanent resident, 20% of your salary goes into a retirement account called CPF, which bears interest ranging from 2.5% to 4% annually. Your take home pay is therefore 80% of your monthly salary. If you are on employment pass/work permit, you do not have to contribute to CPF.
Check this out:
Singapore Expat Guides - FAQ for Singapore expatriates or new expats