There exists a very strong argument that no treaty can violate pre-existing constitutional provisions without being void. The idea that treaties have full force implies that that force comes from somewhere - i.e. the Constitution. Therefore, to draw up a treaty that violates constituional provisions, is to negate the source of that treaty's claim to power.
Of course, interpreting the treaty clause through the 14th Amendment adds another layer of disconnect. But as it was originally written, it wasn't a direct poison pill, and was subject to judicial review vis a vis preexisting constitutional provisions.
On the other hand, Hamilton was a treasonous bastard before there was even a country, and fully deserved the end he received from Burr. Too bad it didn't come sooner.
Disagree there. Ratification by "two thirds of Senators PRESENT" (my emphasis) was the poison pill, as was the placement of the comma in the Supremacy Clause. Patrick Henry was furious about it. He was right.
As a thought experiment, if a treaty was approved by 2/3 of the Senate which proclaimed the Pope as being the supreme and absolute ruler of the US, would that treaty be valid? Could we impose constitutional amendments by conducting a treaty with Burundi?
No. The fact that it's ridiculous to even consider the above means that a treaty is subordinate to the Constitution, and merely exists at the same level as any other federal legislation, and its validity is subordinate to its constitutionality.