i read the treaty clause as no treaty can usurp the constitution... i will have to re read...
When you do reread the supremacy clause, take care with the commas; it may not say what we all want it to mean. You see, we already have treaties on the books for over 70 years whose terms so wildly exceed constitutionally enumerated powers that you have a problem believing what you do. Some were ratified under conditions that were absolutely shocking. Every one has stood the (bogus) test of "settled law."
In fact, some of the Founders took major objection to the way that it was worded, but the Federalists rammed it through anyway because we needed the money and these were the terms our lenders apparently demanded. For some background on that consider this.