Not so! Reason is and must be part of any necessary and sufficient definition of Nature.
Nature is far grander and more wonderful than your absurd caricature of it.
I find nothing whatsoever either original or compelling in your post.
You are certainly correct that it is not original, it is the core argument in C.S. Lewis's book "Miracles." Lewis made this argument in response to materialist philosophy which holds that "the only thing that exists is matter or energy; that all things are composed of material and all phenomena (including consciousness) are the result of material interactions. In other words, matter is the only substance, and reality is identical with the actually occurring states of energy and matter."
If all phenomena, including consciousness, are the result of irrational material interactions that would include Reason, and therefore Reason would not be valid.
However, if Reason stands on its own, independent of natural forces i.e. it is supernatural, then it has the potential of being valid. Now if you want to redefine nature such that consciousness is not included in the definition, and that it is the result of something other than material interactions, you are simply restating the supernaturalist argument and refuting materialism.