There certainly are portions of natural law that have been incorporated into written law. I just don’t see how a good definition of NBC could be derived from any of the theories of Natural Law.
The only self-evident definition I can see is citizen at birth. I think it’s also self-evident that a free people has the right to determine (via their elected leaders) the details of who is granted citizenship at birth.
Are you sure you understand WHY the President of the US and ONLY the President of the US was restricted to Natural Born Citizens?