[El Gato]

“No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.” If they were not worried excessively DURING their lifetimes, they wouldn’t be more worried about AFTER their lifetimes.

What in the heck are you talking about? If they had not exempted "at the time of the Adoption of this Constitution", there would have been no one eligible for the office of President until at least July 4, 1811, 35 years after the Declaration of Independence. No one can be a natural born citizen of a country that did not exist at their birth, although 35 years after other dates would have also been possible, such as the adoption of the Articles of Confederation, or from the signing of the treaty which ended the Revolutionary war and in which the UK recognized the US. But they chose the latest reasonable date.

[Mr Rogers]

There wasn’t a BIRTH requirement. ANYONE who was a citizen at the time of Adoption (“No person except a natural born Citizen, OR a Citizen of the United States, at the time of the Adoption of this Constitution...”) could become President, even if they or their parents had been born elsewhere.