They certainly are, notice that even the contingency of someone born here to citizen parents was not enough for the Founders. They put in an additional requirement to disqualify a child born here and taken abroad unless they had returned for a substantial period of time.
I do not find that the British historic law is as you have stated. Clearly to be natural born required the parents (father) to have been under the allegiance of the king.
"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."
But nevertheless your quotes show how in Britain you could be natural-born even if you were born outside of the country. They put some ifs and buts on there, but our Constitution didn’t have those.
British Statute of 1730:
[A]ll Children born out of the Ligeance of the Crown of England, or of Great Britain, or which shall hereafter be born out of such Ligeance, whose Fathers were or shall be natural-born Subjects of the Crown of England, or of Great Britain, at the Time of the Birth of such Children respectively ... are hereby declared to be natural-born Subjects of the Crown of Great Britain, to all Intents, Constructions and Purposes whatsoever.
Is 14 years really that substantial? The way people go on here about potential foreign allegiance, I highly doubt the anti-Cruz-birthers would ever agree to a mere 14 years residency to qualify for President. They would probably demand no one spent more than one consecutive year overseas. If someone was born in Texas, then moved to Britain for 40 years, then came back here for 14 years and ran for President, under your interpretation of "intent," the founders should've been totally paranoid that person was a foreign agent. Yet they left in this relatively minimal 14-year requirement for U.S. residency.