"What we've done, or attempted to do, is show how science itself is dependent on that which cannot itself be subjected to scientific inquiry, such as the laws of logic."
Yes, methodological naturalism is the philosophical framework of science. It's very easy to understand - it ensures falsifiable explanations. What's your contention?
"We've then posed a probability: given that science depends on something unobservable and antecedent, either we must assume that A) these transcendental principles/facts/truths stand on their own, or B) their very existence points to an ultimate transcendental Cause. From these two choices, we have an irrational one (A) and a rational one (B)."
What transcendental truths? God, et cetra? Those are philosophical propositions that aren't testable. Raising them as falsifications of evolution is meaningless.
"In effect, what we have accomplished is effectively the proving of God's existence by way of elimination, to wit, the absurdity/impossibility of the contrary. The next scientific fact or anecdote someone throws out will rest on the very a prioris that point to that conclusion. Actually, that applies not just to science but to all communication and meaning."
How did you give evidence for God? I don't see it anywhere. Also, dichotomies do not exist in science - elimination and negative arguments against a theory does not validate another *unless* positive evidence is provided for said theory.
"In proving God's existence we have destroyed the possibility of a key logical implication of Darwin's theory, were it true: that there is no need for God for life as we know it. In doing that we have not entirely disproved Darwinism, mind you, but have eliminated one of its primary appeals."
You haven't given evidence for God. Please raise such a contention. And, mind you, they should be falsifiable contentions because to raise philosophical contentions over a non-falsifiable subject is meaningless.
I want to ask you something: Can you offer a proof of the law of non-contradiction?