If you read the article I cited, some states (such as Connecticut) chose to continue to use the term natural born subject, apparently in contravention to your assertion, well into the 1790s.
I looked into the issue expecting to confirm your contention, but I could not find a convincing strict constructionist (that is, the common understanding of the term in effect in 1787) argument in favor of it.
FWIW Jefferson lined out subject and inserted citizen in an early draft of the Declaration of Independence.
A deep thinker, and no fan of the British and it’s monarchy, Jefferson would certainly have thought through the notion of a substantive analogy between the two concepts of citizenship and subjecthood and found it utter folly.
We obviously can do it looking back with 30/20 hindsight but multiple heavy hitter founding fathers (such as Jefferson, Franklin and Washington) certainly had the distinctions pretty well in hand as early as the beginning of the Revolutionary War.
Adams was drew a parallel between NBC and NBS in a circulated draft of the Treaty of Paris in the early 1780s, but seemingly only for diplomatic purposes.
I looked into the issue expecting to confirm your contention, but I could not find a convincing strict constructionist (that is, the common understanding of the term in effect in 1787) argument in favor of it.
The terms are analogous, but built on very different foundations and with very different and well known definitions.
The founders intended that we would be "citizens", and not "subjects." Therefore, they are making it plain that we aren't following British common law on the matter, we are following the normal meaning of Citizen in regards to a Republic.
Citizens descend from citizens. Since the Greek era, "Citizen" meant "Parents are citizens."