Thank you for the engaging reply, and sorry for not responding earlier!
First, let me say that this is by no means a comprehensive look at natural law theory vs. legal positivism, and you bring up excellent points. While I generally agree with you, I'd argue that even natural law theory describes what law is. For example, for Aquinas, a law is an "an ordinance of reason for the common good, made by him who has care of the community, and promulgated." I'd argue that anyone who is attempting to explain what law ought to be necessarily would have to describe what law is in order to make their prescription. You can't evaluate whether something has particular qualities unless you describe what those qualities are in the first place.
Recall that Plato and Socrates both posited that even unjust law still has the form of law. This is a common mischaracterisation of the arguments put forth regarding what is truly law. An arbitrary edict by a ruler would be unjust in classical natural law theory, but nowhere will you find these theorists advocating for unqualified disobedience to those laws. They recognized that those laws still had the form and force of law, even if they were unjust. Martin Luther King, Jr., paraphrasing Aquinas, said as much when he was imprisoned for his civil disobedience.
Additionally, legal positivism does generally avoid discussion of moral content in law. That's not to say that legal positivists don't give the topic thought at all. As you pointed out, they may argue one way or another, but their primary (and many times sole) focus is on identifying laws and their operation. Bentham was notoriously averse to ascribing any moral content to law, and Austin argued that morality was totally inconsequential to the law. The legal realism and law and economics approaches likewise discount any moral content as not being relevant to the discussion of what law is.
They often fail at that, as they have to answer why any law, no matter how well-formulated and efficient, should exist at all. Any evaluation of a law has to take this question into account, and the most that can be said from the legal positivist view is "because the sovereign says it is so."
I don't disagree that the two approaches have their respective strengths, but I'd argue that they can compliment each other and there is some overlap. However, the reason why natural law theory is my favorite is because any discussion of law should start from asking if a law is necessary at all to regulate conduct. Arguably this goes back to the Greeks as well (reconstituted and included by Finnis as one of his seven universal goods; knowledge), as the Stoics felt that pursuing knowledge was a virtue, and this pursuit almost invariably begins with the question why. It's part of the human experience to question. :D
I'm looking forward to your response! Out of curiosity, what is your background? You seem well-versed in jurisprudence, so I'm guessing you've at least studied law, if you're not a lawyer.