Originally Posted by invisible

OK, in the light of the additional information. As I said, only employer can apply for EP and employer needs to be Singapore registered company. You can't register company and then employ yourself there - this does not work. Instead you need to have EntryPass which is entrepreneur type work visa. However EntryPass comes with much more requirements.

My suggestion - read thoroughly MoM website and it probably worth to pay for 1h consultation to someone who specializes in local labor/employment law.