Ahhh, yes... I missed that rather important point... you are LTVP. So, you could not apply for a LOC but you could set up a company (private limited) and then apply for your own EP. Although MOM says you must have an Entrepass, skilled professionals have obtained an EP via this route.
My sense though (and that of others), is that this route is successful only with a track record, and clients or contracts on the ground ready to go. Taking a stab in the dark, trying to find clients, will be less well received. MOM is well aware that scammers will try this route just to stay in the country. No skills, no seed money, no clients, no business plan... no go.
You cannot perform any Singapore based work without a work permit. Even if a local company were willing to apply for an EP for you so could free lance (like me, for example), the problem is justifying your EP when I have no work for you to do. When I used to hire EP's, I always had something for them to do... I have no idea what the response would be if I just merely wanted to hire. And, at what pay rate?
IT/CompSci is a popular degree in Singapore... you would be carefully scrutinized. Note, too, that even if you were to find a company willing to sponsor you, none would do it for less than about 25 percent of your gross... I certainly would not.
I see that you have three options.
a) Become involved as a volunteer... there are many organizations that would drool over the prospect of having a skilled person clean up their IT world.
b) Don't work for clients in Singapore. Work for clients who have offices elsewhere but not Singapore. Work remotely. Singapore law has not totally caught up with telecommuting, but I think this is not an issue, have recommended this course of action to others, and have been supported by attorneys (not that their opinion actually means squat).
c) Use LinkedIn to find a job. The job boards are worthless... so are 98 percent of the recruiters. As I said, though, it will be a tough haul here... reduced demand, and lots of skilled locals and foreigners willing to work for a lot less than you. You really need to have a stand out skill.