Common law is secondary and subordinate to statutory law.
Which brings us right back to your initial contention, natural born [citizenship is] defined by statutes made laws by congress.
Is there any restriction on Congress, or can it theoretically pass an unconstitutional "definition of NBC" law?
By way of hypothetical example, if Congress passed a statute saying Vladimir Putin was an NBC, would that be constitutional? If you view that as ex post facto or naturalization, not natural, then hypothesize Congress decides to be friendly with Mexico, and grants statutory citizenship to persons born in Mexico, to Mexican parents. I know, that's a reach (now, maybe not a generation from now), but we need some hook to debate from.
If there is a restriction on NBC, what is it, and where does it come from? By your terms of this debate, you can't resort to common law, because statutory law is superior.