The OP is quite lengthy and complex. My off the cuff response is that there are a number of things in your proof that do seem problematic to me. The stand-out would be:
Premise 4: If a being exists, its explanation must exist.
If this were not true, science would be impossible. If things "just happened," the observations would not be underlying dynamics, and could neither confirm nor falsify hypotheses. Note that “explanation” has two senses: (1) the fact(s) that make some state of affairs be as it is. (We may or may not know these.) This is the sense I am using. (2) Our attempt to articulate our understanding of (1). This is not the sense I am using here. — Dfpolis
It is to your credit that you state this premise explicitly. But this does not mean that it is unproblematic.
Science does not require that literally everything have explanation. Science only requires that some things have explanation.
Much of physics, as an intellectual project, has been an attempt to determine the fundamental laws of the universe. If there are fundamental laws, by definition they are unexplained. They are simply "brute facts." Today's brute fact may be tomorrow's well explained phenomena (witness what Einstein did for Newtonian gravity), but at any one time there is a base level of explanation. Acceptance of the idea that explanation has to end somewhere is quite widespread among both scientists and philosophers, and science works perfectly well on this level.
I am not going to say that there are brute facts. I am going to say that it is not a self evident truth that there are not - and since you're the one offering the proof, the burden is on you.
If brute facts are not for you, you also do not seem to consider the possibility of antifoundationalist infinite regress, in which every finite explanation has another finite explanation... and so on forever. "Turtles all the way down," as it were.
Another unconsidered possibility here is that of an Escher-esque universe that is ontologically circular. To provide a concrete example of this, consider the following extract from the SEP's entry on time travel:
Gödel. The time traveller steps into an ordinary rocket ship (not a special time machine) and flies off on a certain course. At no point does she disappear (as in Leap) or ‘turn back in time’ (as in Putnam)—yet thanks to the overall structure of spacetime (as conceived in the General Theory of Relativity), the traveller arrives at a point in the past (or future) of her departure. (Compare the way in which someone can travel continuously westwards, and arrive to the east of her departure point, thanks to the overall curved structure of the surface of the earth.) — Smith, Nicholas J.J.
So you can pick up the collected works of Shakespeare from Amazon, go back in time, and hand them to Shakespeare, who is then spared of the chore of ever having to actually write them. It may or may not be allowed by the laws of physics. It may be mind-bending. But it is generally accepted that there is nothing incoherent in this. It is not
a priori clear that it is not possible. And bear in mind, of course, that this is just a concrete, physical example of what I'm talking about.
Finally, the logical possibility of this kind of circularity brings us to premise six. You argue:
Being human explains my ability to think, because that is part of what it is to be human. But, being human does not imply that I exist. If it did, no human could cease existing. — Dfpolis
I'm afraid I can't agree. To be human (or to be anything at all) is to exist. You can't be human if you don't exist. So to be human does imply that you exist. To imply existence is not to imply unceasing existence. If it did, everything that existed would exist forever, which is clearly not the case.
These are just off the cuff thoughts, of course.