If you start from that assumption, you are presupposing Atheism before you begin. Of course we have to make naturalistic assumptions when we study anything scientifically. But just because an assumption is scientifically useful in one specialty doesn’t mean it can be extended into every possible domain. When a doctor is diagnosing a liver disease in a patient he pays no attention to the goals and purposes of that patient. But that doesn’t mean that he is denying that the patient has goals and purposes. Similarly, the fact that Darwinian science must ignore the possibility of goals and purposes for evolution does not give us any reason to believe that evolution lacks goals and purposes

You are also guilty of what I call the Tilde fallacy when you describe the Atheist's task as merely proving God's non-existence. Atheism is itself a theological claim. It doesn't get any special privilege just because it doesn't articulate itself very clearly. Dawkins, to his credit, has articulated Atheist theology quite vividly with his theory of the blind watchmaker. But he doesn’t realize that this very vividness in detail invalidate his attempt to use Occam’s razor to defend Atheism.

I read your entire paper before I posted my first comment, but I concluded that I had already written my response to certain key points in the paper I linked to. I think you would find it helpful when you write about the burden of proof. This is what professional philosophers do: read each other’s papers and footnote them. You have some good ideas, but you are operating pretty much in a vacuum, and are thus to some degree both reinventing the wheel and missing objections to your ideas that have already been written by other people. Dawkins is a kind of genius, but his writing on this particular topic is often very half-baked. (although still worth reading for its originality). I would recommend John Shook for the most intelligent defense of Atheism I have seen.