Is there anything wrong with this approach?
No, not necessarily... but you might be thinking about what you will say to the government authorities when they ask.
First, a brief historical perspective. When the Entrepass was first cooked up in 2004 to attract foreign expertise, it was easy to get. Nobody verified that you really had the capital or that you knew what you were doing. As a result, it was mightily abused by those seeking an easy way into Singapore. Twice the requirements have been tightened, such that only a well-financed, well connected technology company will qualify. And you really wouldn't want an Entrepass anyway because of the onerous requirements for renewal.
The changes to the Entrepass made it nearly impossible for the average professional to start a business in Singapore, and thus, MOM has, on a case by case basis, awarded employment passes to people who start a private limited with a nominee director, then apply for the EP. However, the key to success is to have a the expertise, money, and a line of business that MOM deems "suitable". For example, in the Entrepass thread, there is a person who wanted to use his computer repair talents to form a PC repair company. He was rejected, and while there may have been other issues with his application, I judge that his application was rejected because he would be in direct competition with the zillion single man repair shops you can find at Sim Lim Square and elsewhere.
I judge that your chances of getting an EP would be quite good. You have a successful business. You have paid corporate tax. Your business is a desired technology business. I'd say your nominee director ought to make application for your EP.
You have a few problems, though. First of all, if your Singapore private limited has had revenues, then it has invoiced in Singapore. Unless you can prove up that your nominee director was handling the invoices and putting the deposits in the bank, then somebody has been working for free in Singapore and IRAS doesn't like people working for free.
It all boils down to IRAS definition of "services performed in Singapore". Services performed in Singapore by a foreigner are subject to a withholding tax. You might want to get a throwaway email address and ask IRAS, and I bet that even if you are sitting at a computer in Kenya, writing invoices for your Singapore firm, you will be considered to be performing services in Singapore, especially because no contract payments were made to any other person or entity to perform this task.
Similarly, you are a director. While you are paying corporate tax on a larger net income because you didn't have directors fees expenses, your methods could be seen as a ploy to avoid paying the required withholding taxes for non-resident directors. Further, since you have a nominee director which is essentially a bookkeeping transaction so you can have a Singapore Pte Ltd, IRAS may come back at you saying that you are a managing director or CEO, and since your company is local, the work you do managing the company is subject to Singapore tax at the non-resident rate.
I'm not saying that any of this is going to come to pass... the question of when you are rendering services in Singapore in the age of remote computing and the internet is not an easy one. But, you should for sure check your situation with IRAS before filing for any EP application to ensure that you have not run afoul of the "services performed in Singapore" regulations.
Other than that, I'd say your chances are very good.