Some interesting nuggets in your post...and a couple of potential flies in your ointment. First, there are a lot of crednetialled conservatives who do not agree with your assessment of the Constitutional breach, just as there are a lot who do.
And there's another issue: original intent: the intent of this provision is not to worship a piece of land. It was to protect the idea of America from those who would have more allegiance to another nation. Regardless of where the truth comes down on the technicality, Cruz is in no way in violation of the spirit of the Constitutional provision.
This is a debate I watch from the sidelines, as I have moments where both sides make good points. But when a technicality is in question, I always defer to the intent.
I agree that the eligibility for POTUSA is a matter of concern as expressed by the Founders i.e. no foreign allegiance. Not withstanding all comments and subsequent laws that are argued as to eligibility I look at what is actually in the Constitution, at least the version I have. 1)Section 1 ARTICLE II is explicit and defining in that “No person except a Natural Born Citizen, or a citizen of the United States at the time of the adoption of this Constitution, shall be eligible to the office of President;......”. This is a distinct expression of difference between a ‘citizen’ and a ‘natural born citizen’ and this distinction is carried into ARTICLE I Sections 2 and 3 as to Congresspersons. 2) Amendment XIV Ratified July 9, 1868 Section 1 stipulates “ All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside”. This amendment mentions nothing about such persons being considered as ‘natural born citizens’ only plain ‘citizens’. This is consistent with previous constructions in the original Constitution. One can ask what is missing or discrepant between Article II and Amendment XIV. I will argue that what is such is the factor of parentage which was included in the debates of the Founding Fathers and very wisely so.