There is no record that Hamilton's language was ever the "original language".Yes citizens, just not Natural born citizens eligible to be the President, otherwise the Founding Fathers would have used Hamilton's original language as he had proposed.
The Committee of Detail originally proposed eligibility requirements for the Executive under a Tenth article. See William C. Rives, History of the Life and Times of James Madison, Volume 2.
"The tenth article of the plan reported by the committee of detail provided … that the executive power should be vested in a single magistrate, to be styled the President of the United States ...."
The original eligibility clause did not require a person born a citizen in the country:
Concerning this "Tenth Article" it was stated "At the end of the first section, tenth article, add,'he shall be of the age of thirty five years, and a citizen of the United States, and shall have been an inhabitant thereof for twenty one years.'" WEDNESDAY AUGUST 22. IN CONVENTION. 1787.
On September 4, 1787, the eligibility requirements were amended:
"No person except a natural born citizen or a Citizen of the U. S. at the time of the adoption of this Constitution shall be eligible to the office of President; nor shall any person be elected to that office, who shall be under the age of thirty five years, and who has not been in the whole, at least fourteen years a resident within the U. S."