Scott, great question. Very incisive.
To be clear, I think your question is primarily an epistemic one, something like: “how do we know that God, or the God of the Bible, is the source of moral laws?” I hope I am rephrasing that to accurately convey your meaning.
One way to pursue the answer, might be by showing that a reductio ad absurdum occurs if the idea of God being the ground of the moral law is false. Let’s assume, for example, that there is no God, and therefore no moral law giver. The question then arises:
“Why would we expect on an atheistic, or a materialist view, that there are such things as moral laws, or facts?”
I think the consistent position to take, if God does not exist, is roughly that of Bertrand Russell toward the end of his thinking on the subject, when he assumed a non-cognitivist view of ethics; this entails that we can only have moral emotions vis-a-vis concrete states of affairs, but that there really are no such things as moral facts about the world. Thus, all moral statements are merely expressions of emotion. If there are no moral facts, then there are no true, or false, moral propositions; moral propositions simply have no truth value. So instead of making the claim, “Torturing children for fun is evil,” the emotivist, at best, can say something like “Torturing children for fun…yuck!”
So, first, by means of showing that on atheism there are no moral facts, we show that there can only be moral facts (i.e. cognitivism), if there is something transcendent to the material world. But what kinds of things transcend the material world? I can only think of two, either something like a transcendent personal mind or agent, or an abstract object (like a Platonic form, or the number 2).
Without going into a long proof for why a personal mind is a better explanation for moral facts than platonic objects or the number 2, I think we are justified in saying prima facie that a personal mind seems to be a much better fit as the source of moral facts than an impersonal object called “Justice” that is inexplicably instantiated in the world of concrete particulars, when certain states-of-affairs obtain. That just seems nonsensical.
So, I think we can infer as a best explanation that a transcendent personal mind is indeed the source of objective moral facts. Then, the question emerges of what is this mind like? Here you bring up Descartes’ evil demon. Could it be the case that a moral law giver is more akin to Descartes delusion-inducing daemon, as opposed to the God of the Bible? It’s a good question.
Here I would suggest that God, who by definition is a maximally great Being, would also be a Being who possesses all great-making properties absolutely. Since moral goodness is a great-making property, God would have to be maximally good by the necessity of His own nature. And, as a maximally great and maximally good Being, God would not be able to contradict His own greatness, (otherwise He would not be the Being we are talking about, but some lesser Being). Thus, God cannot command that which is contrary to His nature, which is itself Goodness. Therefore, God can not command evil. If God cannot command evil, then He does not command it.
Further, if God does not command evil, and if we are convinced from other independent lines of evidence that Jesus Christ is God, and that Jesus affirmed the truth of the Bible, then we can deduce that the Bible tells us about the moral law by showing us who the true God is, who Himself is maximally Good. So maybe we could develop an argument:
Premise 1: God, as a maximally great Being, is maximally Good
Premise 2: A maximally good God cannot command evil
Premise 3: Therefore God does not command evil
Premise 4: Jesus is God
Premise 5: Jesus affirmed the truth of the Bible (Hebrew Bible)
Premise 6: Therefore, the Bible tells us the truth about God
Premise 7: If the Bible tells us the truth about God, then it tells us the truth about the moral law giver
Premise 8: If the Bible tells us the truth about the moral law giver, it tells us the truth about the moral law
Premise 9: Therefore, the Bible tells us the truth about the moral law.
I’m sure there are some points to quibble with here, since no argument on this or any other matter is flawless, but maybe this offers us a starting point for further discussion.