You are pretty much screwed right now without the large down payment. And going FHA right now is out of the question with their getting stricter everyday guidelines. I have been in the mortgage business for more than 10 years and specialized in FHA/VA Loans but when everything changed 24 months ago I lost all my LO's working for me because the lenders slammed the door on the easy lending guidelines.
In a way I am kinda glad because anybody who could fog a mirror could buy a home. We used to have AE's come in and tell us "how" to get a loan approved on the subprime/Alt-A side of things which is where you would fall being "self employed". Unfortunately it is where me and my wife fall as well with me slinging Dildos now and her owning a mortgage processing company. I will get back into mortgages because it does pay well but I like doing this job so far.
At the moment I think you are out of luck on buying a home with current guidelines unless you have atleast 20% down. But if you were illegal and have a green card or been using the same social for 2 years then you can do a I-10 all day long AND get down payment assistance on top of that. It sucks when the government still does these loans but can't do it for tax paying legal residents
but thats the way the cookie crumbles.
good luck