Reid v. Covert is dicta. Show me one treaty that has been thrown out by the courts. There are dozens of them whose terms exceed Constitutional limits.
Exceeding constitutional limits is not the same as abrogating individual constitutional rights. The burden of proof is to show one treaty that ever successfully made a direct attack on a fundamental individual right recognized as such by the Constitution. If you know if such a case, I would be interested to hear of it. And Covert, as I recall, did not pull treaty inferiority out of thin air. Inartful distinctions between dicta and holding have led to some unpleasant surprises when attempted in legal practice. However, to be fair to you, I will review it and get back to you. I am presently being held captive by a kitchen remodeling project and don’t have immediate access to my usual research tools. :)