The answer I think I once heard to this is that in truth even these type of commandments are in essence rooted in the Torah’s definitive moral code.
Totally not. The Brisker Rov (and the Shagas Aryeh, IIRC) bring that the Torah is an override of “moral” code, and the general good of society. The examples given is lending with interest, which is good for the economy, and Assisted suicide. Both may be allowed in Noahide law (IIRC), but not in Torah law. The Brisker Rov explains (and I don’t remember where) that Noahide law is meant to create a “moral” society, while Torah law is following the will of Hashem over what you would think is the right thing to do.