“The founders considered using the simpler, single word “born,” but rejected it after much deliberation (about the importance of exclusive allegiance) in favor of the phrase “natural born,” so an honest person cannot claim that the two mean the same thing.”
Actually, there was no debate held on that section. As to what it means, the following decision discusses it at great length:
http://www.law.cornell.edu/supremecourt/text/169/649
“It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore every child born in England of alien parents was a natural-born subject unless the child of an ambassador or other diplomatic agent of a foreign State or of an alien enemy in hostile occupation of the place where the child was born.
III. The same rule was in force in all the English Colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the Constitution as originally established.”
In your own words, what is the additional restriction of meaning that the word "natural" adds to the phrase natural born Citizen over that of plain "born citizen?"
If you claim that the word adds no additional meaning, then why did the founders bother to add it to a document for which each section, phrase and sometimes individual word was deliberated and debated over for months?
The Founders were not a monolithic whole. There were disagreements among the Founders on practically every substantive constitutional issue and many issues were resolved only by compromise. After all, “politics is the art of compromise” and many Founders were politicians. For example The Founders decided on direct popular election of the House of Representatives only and Senators were indirectly elected by state legislatures (The Connecticut Compromise of 1787). In 1913, the Founders’ plan for the structure of the federal government was abolished by the 17th Amendment and since then Senators have been popularly elected.
The Founders made it difficult, but not impossible to change their original thinking on any constitutional issue via the amendment process.
The Supreme Court said in 1875 that: “The Constitution does not say, in words, who shall be natural born citizens. Resort must be had elsewhere to determine that.”—Minor v. Happersett
Since 1868 and the adoption of the citizenship clause of the 14th Amendment, only two classes of citizens have existed, born citizens and naturalized citizens. There is no category “natural born citizen” that is separate and distinct from “Citizen of the United States at Birth.” They are one and the same.
The category “Born Citizens” does make provision for persons born “over the sea” (as it says in the Naturalization Act of 1790) to be Citizens of the United States at Birth. That continues today.