yep, you are right... it is VERY difficult to do, but not impossible.
you need to set up a company and try to sponsor yourself for the work visa. (the company you own sponsors your visa, so you in effect sign as your own sponsor). you will most likely have more luck with a limited company, where the company and you are separate legal identities.
i went this route back in 1998. back then, it was difficult. NOW, i would think it is even more so. you need to prove that you earn enough $ to make a go of the company. you need a solid business plan. you need to have clients ready to sign up and commit for an extended period of time. you need profit & loss accounts and turnover. you need all the "books" set up properly.
beware though.... if you take on clients while on your current visa, you are breaking the law. so, you CANNOT say that i've been teaching so and so for x period of time and they have agreed to continue with the lessons. also, your new company will basically have to provide all of the documentation that your current employer provided to secure your visa. you need to show that you are actually adding to the hk economy. if you can employ a local, that's even better.
also, something to keep in mind (and a problem i had when trying to sponsor someone else to come to work for me) if you are going to your clients' homes/offices (like i do) then it isn't really necessary for you to have an office of your own. try explaining that to immig. i did MANY times. they just couldn't wrap their heads around the fact that an office of your own isn't necessary.
it can get kind of tricky. if i were you, i'd call one of the immigration consultants and ask them in detail what you'd need to do in order to make a go of it.
keep in mind that the setting up of the company, business registration etc. for a ltd company will set you back close to $7-8k. a limited company MUST be audited every year as well. that will set you back another $5k or so per year, plus the cost of the accountant is about the same, $5k (for a VERY small company).
this post wasn't meant negatively, just a few words of caution, it's not as easy as it may seem!
good luck, whatever you decide to do!
(where do you teach? i may be looking for someone by summer to work in my new tutorial centre/playgroup.)