I’ll just make a few more points. First, the naturalist has more than just science at her disposal. She has philosophy too, and philosophy needn’t be so reductive. Still, the question would remain whether philosophy can provide ultimate answers that avoid the problems with scientific and religious ones.

Second, you’re doing something very similar to the naturalist when you say, “Science describes how things function in a particular context – it doesn’t explain why we have that context. In other words science can’t explain why we have those particular laws of nature that permitted life.”

You’re saying God’s existence isn’t an inexplicable fact because he’s logically necessary. So you’re presupposing the laws of logic. Why, then, those laws rather than others? Doesn’t God create logic? Is logic more fundamental than God (as the Fates seemed more fundamental than the Greek’s Olympian gods)? This is like falling into the Euthyphro dilemma by saying that God says some things are good because they’re independently so.

Again, to get around the problem of positing an inexplicable fact, you’re doing what the naturalist does: you’re engaging in a reductive explanation of God by positing the laws of logic to explain why God exists.

Third, you’re really making two separate arguments, one from the physical constants, and an analytical argument about that trilemma you posit. It’s not actually logic you’re appealing to so much as it’s your a priori analysis of the relevant options (a necessary being, an inexplicable fact, or an infinite series). This is an appeal, rather, to human imagination or perhaps just to yours. But I doubt you want to imply that human imagination or conceptual prowess is more fundamental than God’s existence. That would seem hubristic from a religious perspective.

I know you think we’re like God in terms of our agency, but the question is whether that analogy is strong or weak.