So is it your contention that Rawle was NOT speaking solely about only those living "at the time the Constitution was adopted?
Absolutely. He spoke about both, but when he spoke about those who were being "subsequently born a citizen of a state," every person who became "at the moment of his birth a citizen of the United States," and "every person born within the United States," it's crystal clear that he was talking about those born after the adoption of the Constitution.
So you have added still another Constitution-twister fallacy.
Fallacy: When Rawle said, "Therefore every person born within the United States, its territories or districts, whether the parents are citizens or aliens, is a natural born citizen in the sense of the Constitution, and entitled to all the rights and privileges appertaining to that capacity," he was speaking of people who were "grandfathered in" to Presidential eligibility by virtue of having been citizens of the United States at the time the Constitution was adopted.
Truth: It's completely clear that Rawle was talking about people born after the adoption of the Constitution.
"The citizens of each state constituted the citizens of the United States when the Constitution was adopted.
The rights which appertained to them as citizens of those respective commonwealths, accompanied them in the formation of the great, compound commonwealth which ensued. They became citizens of the latter, without ceasing to be citizens of the former, and he who was subsequently [that is, AFTER the adoption of the Constitution] born a citizen of a state, became at the moment of his birth a citizen of the United States. Therefore every person born within the United States, its territories or districts, whether the parents are citizens or aliens, is a natural born citizen in the sense of the Constitution, and entitled to all the rights and privileges appertaining to that capacity.