This was tossed aside years ago. Standard doctrine now is is that treaties are contracts between governments, and laws define actions of citizens within states. There is no longer any credence to that "supreme law of the land" BS..
Example: the 1977 Carter Canal Treaty said I wouldn't have to pay any income tax. The IRS said the treaty doesn't matter. We took it all the way up the appeals court and the majority voted against the minority (Scalia) saying we were right. Scalia got named to the SCOTUS and with the IRS he managed to overturn the appeals court ruling on the SC level. Scalia didn't know what a recusal was back then.
Bottom line: treaties are all well and good but lawmakers can and do ignore them inside the US. Treaties do not trump the Constitution Hell, they can't even trump the IRS!
I hope to hell you're right about that in the general case, mate.