It seems to me that you have created a one-time exception that gets yourself out of the infinite regress that this line of thought leads to. All it does, however, is to raise another question to replace the original one: why is God necessary?
I think it does exactly that, which is supposes a one-time exception to get out of infinite regress. But, I mean, if God exists, that's how it is. So the story doesn't seem incoherent. As for asking why is God necessary, I think that is a misplaced question. God's necessity wouldn't derive from something else, because then it wouldn't be necessity (just another derived contingency). The starting point is that something necessary has to be the basis of the rest of the stuff, that's it.
Not being obviously incoherent is not an argument for that belief being correct; it is merely the very minimum a belief has to achieve to avoid being summarily dismissed for being irrational.
I can understand why you would like the question of why God is necessary to be "misplaced" (which is a euphemism for what, exactly? It is no less coherent than the other questions being entertained here), but, with your 'that's it", you are simply refusing to look further than the answer you wanted.
Furthermore, as I am sure you are aware, 'God' is a loaded term, on which has been heaped a huge amount of conceptual baggage. Therefore, I assume you chose to write 'God', rather than some more neutral term such as 'necessary cause', for some purpose - but what? Your argument for there being a necessary cause would not offer any reason to justify any of that baggage.
I agree with this, but we don't really know if the universe is God using this infinite regress definition.
The cool part about this definition of God, is that it necessitates the existence by definition, and gives a falsifiable hypothesis.
Continuing with this definition, current cosmological theories would then imply that the Big Bang is God. Though this explanation of the beginning of everything leaves me unsatisfied. It just feels like something else kicked everything off.
We really need a way to peer behind the Event Horizon of the Big Bang, which we obviously can't do empirically, so we are stuck using logical deductions.
I personally think studying pure math and some of the more untested physics theories like String Theory, and Stephen Wolfram's physics project give a lot of food for thought.
Enumerating every possible pattern, while computationally infeasible, still paints an interesting landscape, even granting how little of it we can describe.
Defining God to be whatever is assumed to be necessary is the opposite of a falsifiable hypothesis.
You say we are stuck with logical deductions, but the thing about them is that they are no more true than are their premises, so analytical metaphysics grounds out in a personal and subjective choice of axioms (subjective in the sense that no-one else is logically compelled to accept them.)
I think if we found the beginning causal chain, then that would be falsifiable... theoretically.
Assuming God = Beginning of the causal chain,
Finding this prime mover becomes a tangible physical hypothesis.
I don't think most religious people would agree with this definition of God though.
Also, if the information needed to confirm the beginning of the causal chain is locked behind an Event Horizon, then I don't know what to conclude about this.
I think it's possible to build a model in our slice of the universe that can let us peer beyond such limitations. But I can't be sure.