"Appear"? "Original intent"? You don't and cannot know entirely said intent, so you admit that you are not qualified to judge objectively by adding "appear" along with your "common man" standard, which is subjective in every case, including yours. Unfortunately for that case as regards public intent, there was a large fraction of the people who did not care about or support either the Revolution or the Constitution. So just what the "common man" thought was being sold was subjective, many may have in fact included those who understood Patrick Henry's rat while others thought it was a necessary evil. The problem for you is, what does it actually SAY as opposed to how it was sold. There was intent for public consumption and there was intent for public benefit; i.e., survival of the nation as an independent entity.
It was the political class of its day that brought this about. Hence, their hidden agenda IS of import to you as regards what it says LEGALLY, not just what it means to you. The Constitution clearly states that treaties are co-equal to it. The problem is powers of enforcement, which you think are limited but the treaties indicate otherwise. Better parse that comma in the Supremacy Clause both ways or you just won't get it. Read the article or stay ignorant. Your choice. I'm done with you until you have.
"It is the right and responsibility of every man to read and interpret the Constitution for himself." - Thomas Jefferson.
That means that the federal government is bound by whatever treaties it signs, just as it is bound by the Constitution. Just as the Constitution conveys no authority for Congress to grant itself new powers, neither can any treaty.