So what law do you want to use to define the term “natural born”?
The same two the Founders spent public money on to use in Congress, since they say basically the same thing-
Journal of the Senate of the United States of America / Monday / March 10, 1794 / Volume 2 / page 44
Ordered, That the Secretary purchase Blackstone's Commentaries, and Vattel's Law of Nature and Nations, for the use of the Senate.
http://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=002/llsj002.db&recNum=42&itemLink=D?hlaw:13:./temp/~ammem_LF5V::%230020043&linkText=1
The Law of Nations; Or, Principles of the Law of Nature Applied to the Conduct and Affairs of Nations and Sovereigns, Emmerich De Vattel
The natives, or natural-born citizens, are those born in the country, of parents who are citizens.
William Blackstone, Commentaries on the Laws of England
Natural-born subjects are such as are born within the dominions of the crown of England; that is, within the ligeance, or, as it is generally called, the allegiance, of the king;
The dominion of the crown is the country within it's jurisdiction, and citizenship is a product of Allegiance, so you can't be born into 'the Allegiance of the King' unless your parents already have theirs.
The only difference between the two is that the Law of Nations/Nature means the States are Sovereign, while English law makes the federal government 'king'.
The power given to the general government in the Constitution was to make a uniform rule of naturalization for the States to follow, NOT determine who is or is not natural-born.
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It's been fun, but I have my doubts any amount of words will change an already made-up mind, so you have a great day.