President George Washington and almost half of the Framers of the Constitution say you're wrong.
And James Bayard, backed by Chief Justice John Marshall, Supreme Court Justice Joseph Story, Chancellor James Kent, and other leading legal experts of the early United States - says absolutely and categorically that you're wrong.
And of course John Bingham himself NEVER, EVER said that persons born US citizens abroad were ineligible. He NEVER, EVER said it took birth on US soil plus citizen parents to be a natural born citizen. You can only twist his words to what you want them to have meant, when he described "natural born citizens" as "citizens by birth," when he himself stood absolutely silent and without any objection at all in the House chamber while James Falconer Wilson quoted Rawle's quote that absolutely contradicts your birther crap, and when he and our other Congressmen deliberately dropped the wording you think "proves" your point and substituted "and subject to the jurisdiction thereof."
So why don't you take your anti-Ted-Cruz, trolling birther crap some place else?
Everything you have stated is utter nonsense. Ted Cruz is not eligible. He was born on foreign soil outside the jurisdiction of the United States. A dual citizen is not a natural born Citizen.