Naturalization, to be precise about it. Your argument depends on rules of naturalization being controlling authority to define natural born citizen.
If I understand your argument, since rules of naturalization is a power of Congress, the definition of "natural born citizen" is also a power of Congress. My point is that under that source of authority, the definition of "natural born citizen" is not fixed. Whatever "natural born citizen" meant 50 years ago is different today (the rules of naturalization as applied to foreign born children of a citizen parent have changed), and can be different again tomorrow. The phrase "natural born citizen" has no independent/constitutional definition, it depends on congress to define it.
Now, whether or not that elevates the congressional enactment to be above the constitution is just argument over the intention of the founders. If the founders intended "natural born citizen" to have a fixed meaning, then giving congress the power to change the meaning would be I submit, elevating congress/statute over the constitution. On the other hand, if you are right, then the founders never intended "natural born citizen" to have a fixed meaning.
What the FF intended was that We the People have the ability to make laws through our elected representatives and to amend our Constitution if we believed it necessary to do so.
The FF intended that the Constitution be the supreme law of the land AND that anything not prohibited by it or directed to a particular federal authority be left to the People to decide. (10th A)
There is no meaning of “natural born citizen” provided by the Constitution.
Therefore, it’s the domain of the Congress, since naturalization is the domain of Congress. To say who must be naturalized you must determine who does not.