Interesting. What is more interesting to me is that the Framers used the words specifically “natural born” to differentiate from just plain “citizen.” Only the eligibility to serve as president and command in chief requires this designation. Citizen is not the question. Natural born citizen as required by the constitution is the point.
I will admit there are many interesting arguments prsented, but the only real issue goes back to the old KISS (Keep it simple, stupid) Cruz was NOT born in the US of Two Citizen parents, therefore he is NOT a natural born citizen.
I agree with your formulation, but was pondering how thin a connection to the US is permitted by US laws that confer citizenship. Pretty thin connection!