No, the founders were not demanding sole nationality. Otherwise, some other nation could interfere with US Presidential elections by simply granting citizenship to their country.
What the founders were attempting is to define a condition that would show positive allegiance to the United States. Congress could establish a greater set of rules by saying NBC means Citizen parents, born in the US, and resided X years prior to the age of majority is the only condition that qualifies as NBC.
My point is simply this. The Constitution clearly enumerates that Congress has the authority and Congress needs to fix this.
You misrepresent your point by not stating that Congress' authority applies to ALIENS, or foreigners, and not towards citizens.
Incorrect. You would need to pass a Constitutional Amendment to repeal the natural born Citizenship clause in Article II. Not going to happen.