Great post, but I would suggest a couple clarifications.
First, before you can reasonably ask about the existence of God, you must make clear what you mean by 'God'. Since there are many different notions of what God is, you need to be specific. It could be, e.g., that the Jews' notion of Yaweh is the same as the Muslims' notion of Allah. But to someone else, God might simply be the first cause. Arguing the existence of these different notions would take very different courses.
It still seems to me that it would be useful to list a set of attributes that God may or may not have, and then argue the existence of a God with or without each of these attributes. For example, for the attribute of perfection, that Stanley raised, the question would become, Is God perfect? or Does a perfect God exist? or simply, Does perfection exist?
I think most religions would claim that God is perfect, infinite, omnipotent, etc. -- in short, almighty. But I think the God that athiests deny, and that scientists try to explain away, is a transcendent sentient God, that wouldn't necessarily have to be perfect or infinite. That would be simply a God that "lives" somewhere inaccessible to scientific observation and experiment, and who knows about us humans and takes an interest in us.
So, for example, my personal belief in the existence of God, is that I think a transcendent sentient God exists, but that God is not almighty in any sense other than that he is unimagineably powerful, awesome, capable, good, loving, etc.
The second point is the starting point of the Cogito. Harv pointed out to me a long time ago that we can't be sure about the assertion, "I think", because the very notion of "I" is not clearly understood. If you remove any assumptions about the nature of the "I", you are left simply with "Thought happens". In my view, that is the only undeniable assertion one can make.
(I recently read Descartes and discovered that he, too, had the same doubts about the meaning of the "I" so it isn't as if he overlooked the difficulty.)
In my personal view, as you have already heard more times than you care to, I posit that God is the "I" in the Cogito, and that God is the only thing that exists. All the rest is nothing more than thoughts in the mind of God as Berkeley figured out.
Thus, God's rejoinder to Abraham would be, "You're kidding yourself thinking that you are a "knower". I am the only "knower" around here. I am that I am."