I had to think about this one for a while because what it comes down to is that you would like to know if there is a way to buy yourself into a residency permit.
If you are seriously independent (upwards of SGD 2.5 million available cash), you could apply for the Global Investor Programme - http://www.contactsingapore.sg/Library/ ... t%20EN.pdf
With respect to starting your own business, read my thread about the Entrepass in the Business forum, the threads about starting a business and the LOC, and search my threads for "business". My guess is that with a decent business plan, and the kind of experience and cash you have, you could probably win approval to create a private limited, obtain an EP through it, and thereby get the residency permit you want.
The problem is that if you are not earning enough through your company to pay salaries and expenses you will run into problems when it comes time for EP renewal... the kimono will be opened for all to see that your company is really just a ruse to get a residency permit.
Your third option is potentially viable. The big problem is finding the right company. If I were still running my project management company I might consider it. You need a relatively small company that has an inside into clients that would generate projects for which you qualify. And, you can't cost the company any money.
You could probably keep this arrangement running for a longer period of time as profits from other parts of the company activities would mask the fact that you are really being paid out of invested capital and are not bringing in revenue in excess of your expenses. But, it could work.