Is it really so hard for poor international applicants? Where would it be easier?

I am an Indian belonging to a family which earns less than 20,000$ a year.

I have been told by many that getting funding to study in American schools is very difficult in general for international students. Looking at the CDS of the places I'm applying to, I think what really is difficult is getting into the schools as an international applicant.

I really believe that my performance in high school as well as the essays I've written so far are great for getting into these schools, if only I had been rich enough, which I am not.

I am a bit ambitious, applying to Stanford, Cornell, Harvey Mudd, Pomona, Carleton. I still haven't finalised the list of places I'd be applying to. That is where I'd like to get someone's help, and I'm looking for that here. I will not be able to afford external counsellors, and my school doesn't have one.

Please suggest some places where I'd be a good fit and, most importantly, am likely get funded. I'm looking forward to be a CS (or something like Stanford's CS+X) major. General advice and suggestions are welcome.

PS: I am not looking for any 'safety' school really because I believe I'm better off staying and studying here in India than getting into a safety school.