The analysis--and conclusion may be correct--but as a Founding Father, aren't you ignoring the fact that we are (or were) citizens of the respective States and not (or were not) citizens of the United States? The use of "persons" allow[s,ed] US to be represented.
That was indeed the situation until the present Constitution was adopted. The United States was originally a Confederation of States, and was going down in flames eleven years after Independence.