Agree with @thumper1.
Why does it have to be those universities that happen to be the most competitive in the US?
You are on a prestige hunt and that does not bode well for any future acceptances.
Those departments are small. There are over two thousand colleges and universities, in the US, that may have hundreds, if not thousands of students vying for specialty Ph.D.'s
The schools limit their budgets to known students and researchers currently doing specific research.
Are there no research institutions in your country???