Do all the moral precepts of the Old Law belong to the law of nature?

It seems that not all the moral precepts [of the Old Law] belong to the law of nature:

Objection 1:  Ecclesiasticus 17:9 says, “He gave them teaching, and the law of life for an inheritance.”  But teaching (doctrina) is distinct from the law of nature, since the law of nature is not taught, but is instead had by natural instinct (ex naturali instinctu).  Therefore, not all the moral precepts belong to the law of nature.

Objection 2:  Divine law is more perfect than human law.  But human law adds some things pertaining to good morals to what belongs to the law of nature; this is clear from the fact that the law of nature is the same for everyone, whereas diverse moral practices have been instituted among diverse peoples.  Therefore, a fortiori, it was fitting for divine law to add some things pertaining to good morals over and beyond the law of nature.

Objection 3:  Just as reason induces men to good morals, so too does faith; hence, Galatians 5:6 says, “Faith works through love.”  But faith is not included in the law of nature, since what belongs to the Faith lies beyond natural reason.  Therefore, not every moral precept of divine law belongs to the law of nature.

But contrary to this:  In Romans 2:14 the Apostle says, “The Gentiles, who have not the Law, do by nature those things that are of the Law.”  This has to be understood as referring to things that have to do with good morals.  Therefore, all the moral precepts of the Law belong to the law of nature.

I respond:  The moral precepts—as opposed to the ceremonial and judicial precepts—concern things that in their own right (secundum se) have to do with good morals.
Now since human morals are set apart by their relation to reason, which is the proper principle of human acts, morals are called good when they are consonant with reason and bad when they are at variance with reason.  And just as every judgment of speculative reason stems from the natural cognition of first principles, so too, as was explained above (q. 94, a. 2), every judgment of practical reason stems from naturally known principles on the basis of which one can proceed to make judgments in various ways about various matters.
For instance, among human acts there are some so clear that they can immediately, with very little consideration, be approved of or disapproved of on the basis of these general first principles.
By contrast, there are others such that judging them requires an extensive consideration of various circumstances that only the wise, and not just anyone, can carefully investigate—in the way that the role of investigating the particular conclusions of the sciences falls only to the philosophers and not to just anyone.
Lastly, there are some acts such that in order for a man to pass judgment on them, he needs to be assisted by divine teaching.  This is the cases with the things that have to be taken on faith (credenda).
So, then, it is clear that since (a) the moral precepts concern matters that belong to good morals, and (b) these good morals are consonant with reason, and (c) every one of human reason’s judgments stems in some way or other from natural reason, it must be the case that all the moral precepts belong to the law of nature—though in different ways.
For there are some precepts of a sort that every man’s natural reason judges immediately and per se that such‑and‑such should be done or should not be done, e.g., “Honor your father and your mother,” “You shall not kill,” and “You shall not steal” (Exodus 20:12‑15).  Precepts of this sort belong to the law of nature absolutely speaking.
But other precepts are such that it is the wise who, after a more subtle investigation by reason, judge that they should be observed.  And these precepts belong to the law of nature, but in such a way that they require the sort of teaching by which the young are instructed by the wise—e.g., “Stand up in the presence of a hoary head, and honor the elderly person” (Leviticus 19:32), and others of this sort.
Finally, there are other precepts such that in order to make a judgment about them, human reason needs divine instruction, through which we learn about divine things, e.g., “You shall not make for yourself a graven image, nor any likeness ..... nor shall you take the name of your God in vain” (Exodus 20:4,7).

Reply to objection 1 and objection 2 and objection 3:  The replies to the objections are clear from has been said.