…You claim that God freely created logic and therefore transcends the rules of logic. Now why do you think that? Such a view, after all, is not the mainstream view of Christian theology but lies on the extremist fringe. By far and away most Christian theologians do not think that God has the power to do what is logically impossible or to have created different rules of logic so that what is logically impossible would have been logically possible. You seem to give two justifications for such a radical view: (i) God is omnipotent, and (ii) God is the creator of everything.
But as for (i) there is no reason to construe omnipotence to entail the ability to do the logically impossible (take a look at my Brown Bear and Red Goose book, “God Is All-Powerful”–or the relevant section in Philosophical Foundations!). Logical impossibilities like creating a round square or making a rock too heavy for God to lift are not “things” at all but just contradictory combinations of words. Moreover, if you do think that God can do logical impossibilities, then the problem of evil immediately evaporates, for then God can bring it about that both evil exists and He exists, even though that is logically impossible! Even if evil proves that it is logically impossible that God exists, God can bring it about that He does not exist and that He exists, so no problem!
As for (ii) I don’t think that the laws of logic are things, any more than are holes, Wednesdays, or numbers. So while God certainly is the Creator of all that exists, He needn’t be thought to be the Creator of logic’s laws. Rather I’d say that the laws of logic are a description of the functioning of God’s mind. The Bible says, “In the beginning was the Logos (word, reason), and the Logos was with God and the Logos was God” (John 1.1). God is the supremely logical thinker, and the laws of logic are a reflection of His mind, just as the moral law is a reflection of His character. Just as God did not arbitrarily make up the moral law, so He did not arbitrarily make up the laws of logic.
What you’re missing, then, is the third way between the horns of your dilemma: the laws of logic are neither arbitrarily willed by God nor is He subservient to them; rather they are grounded in His nature.