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There is no approval of polygamy in the Bible at all, even in the special case of levirate marriage.

You're being intentionally obtuse. How is this not approval?

Deuteronomy 21:15 If a man have two wives, one beloved, and another hated, and they have born him children, both the beloved and the hated; and if the firstborn son be hers that was hated: 21:16 Then it shall be, when he maketh his sons to inherit that which he hath, that he may not make the son of the beloved firstborn before the son of the hated, which is indeed the firstborn: 21:17 But he shall acknowledge the son of the hated for the firstborn, by giving him a double portion of all that he hath: for he is the beginning of his strength; the right of the firstborn is his.

What is it about "if a man have two wives" do you find challenging? Sheesh. Knock this off. As Christians we're supposed to be searching for the Truth. You're behaving like a liberal who's confronted with some reality that doesn't fit into a preconceived narrative.

Nor is there any mention of so-called “Natural Law” in the Bible;

Wrong again, Troll Folk.

Romans 2:14 For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: 15 Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another

The Natural Law contains the basic rules of morality that don't need Scripture for proof because they've already been "written our hearts" by God Himself. It's what C.S. Lewis called the "Tao." You don't need a Bible to tell you that stealing is wrong. That's the Natural Law. As St. Augustine put it:

Theft is surely punished by your law, O Lord, and by the law that is written in the human heart, the law that iniquity itself does not efface.