You can not get a truth from a proposition. So, a moral nihilist would say he is a non-cognitivist in that case. Truths are not repeatable and don't reside in logical abstraction detached from worldly experience. If you study the complete history of metaphysics you'll see that what passes for philosophy today is just one big comedy/horror show.

suggest that morality can be derived directly from either reason or from logical laws

That just comes from belief in an eternal realm of immutable Truths. Christians believed that Reason was part of the spirit and transcended the material. That's actually BS but it is something pious atheists like to hold true to base their degenerate egalitarian nonsense on -- Gay Rights, Human Rights and the like -- not really serious philosophy i.e. Reason is not universal.

law of noncontradiction?

I do not contradict myself — that is a temporal prejudice.

-- Ernst Jünger

Have you read Heidegger? He clears up all these silly errors concerning things and time etc. Truth actually has to have womanly qualities for a society to be healthy, this is something I was thinking about the other day and it does check out with Nietzsche and Heidegger too -

"SUPPOSING that Truth is a woman—what then?"

There's good reason why Nietzsche began a book with those words!

Heidegger said the same thing when he said Aletheia is a Goddess, but I think he made that up although that doesn't really matter; truth is a woman and that's all that matters. Polytheistic 'accordance' aligns the spiritual, Being with the material, Becoming and puts man back in-the-world with heightened mythical experience. It also closes the cycle of philosophy that began with Plato and puts "us" (obviously there's a hell of a lot of stragglers here that still believe in a monotheism -- "God is not dead," um no) back to the task (the melding of practise and theory) of thinking-in-the-world.

TL;DR truth is a woman, hence moral nihilism. It is not MUH RATIONAL TRANSGENDERED LOGIC!