That, is the dilemma...what did they mean?
There is no question that a child born of two citizen parents and on the soil is Natural Born, other configurations cause doubt and questionable allegiance.
That's it in a nut shell, it's my opinion and what I believe the Founders intended.
You have shown no evidence to the contrary, ergo your opinion is as good as mine.
Notice there is a discussion here without calling names?
the children of the king's embassadors born abroad were always held to be natural subjects: for as the father, though in a foreign country, owes not even a local allegiance to the prince to whom he is sent; so, with regard to the son also, he was held (by a kind of postliminium) to be born under the king of England's allegiance, represented by his father, the embassador. To encourage also foreign commerce, it was enacted by statute 25 Edw. III. st. 2. that all children born abroad, provided both their parents were at the time of the birth in allegiance to the king, and the mother had passed the seas by her husband's consent, might inherit as if born in England: and accordingly it hath been so adjudged in behalf of merchants. But by several more modern statutes these restrictions are still farther taken off: so that all children, born out of the king's ligeance, whose fathers were natural-born subjects, are now natural-born subjects themselves, to all intents and purposes, without any exception; unless their said fathers were attainted, or banished beyond sea, for high treason; or were then in the service of a prince at enmity with Great Britain
The underlined almost line by line in concord with the logic and intent of the naturalization laws of 1790 and 1795.