I think that this is the misunderstanding; Natural Law is not just "what humans do, have done, and always will do". For Aquinas, "
The natural inclination of humans to acheive their proper end through reason and free will is the natural law. Formally defined, the Natural Law is humans' participation in the Eternal Law, through reason and will. Humans actively participate in the eternal law of God (the governance of the world) by using reason in conformity with the Natural Law to discern what is good and evil."
http://www.aquinasonline.com/Topics/natlaw.html
Emphasis is my own. There can be no proper understanding of Thomistic Natural Law without mentioning man's proper end,
telos, or his Final Cause (see
here). I bring this up because, though it is a distinction, it is an important one that eliminates many common objections.
On to this, I don't think you're correct in saying that the soul is a supernatural construct. At least not in the way that Aquinas and Aristotle speak of the soul and nature. Specifically
here, we see that for Aquinas the soul the form of the body. Now with what was in the second link above about the 4 Causes, we see that the soul is not a supernatural (above nature) idea. Rather it is the formal cause of our being, with the body being the material cause.
But all of this ignores the fact that Aquinas' and Aristotle's ideas of the Natural Law are firmly rooted in metaphysics. Metaphysics gives the foundation for philosophy, which gives us the ability to reason things such as how to govern the
polis.
But really I'm just making a fool of myself. Whiskey can explain this all much better than I can, and I've probably already made several mistakes in my explanation. But I could not let you say something as absurd as Aquinas' belief in God, which is contra Natural Law.