TREATY EMBROILMENT IS SO DANGEROUS AND SO IMPORTANT, THAT TO FURTHER LIMIT AND RESTRICT THEIR MAKING, ARTICLE II, SECTION 2, PARAGRAPH 2 ORDERS THAT THE PRESIDENT: "...SHALL HAVE POWER, BY AND WITH THE ADVICE AND CONSENT OF THE SENATE, TO MAKE TREATIES, PROVIDED TWO THIRDS OF THE SENATORS PRESENT CONCUR; [EMPHASIS ADDED.]"
It seems as though the 2/3 present statement agrees with my original assertion...
Not that I know for certain that text is authoritative.
I did some reading and it does sound like there 2/3rds present is relating to the quorum requirement. If worse came to worse, the absent members could be compelled to attend for the ratification process (if subversion was indeed the aim, I don’t see why anyone present would want to compel members that would vote contrary anyhow).
I could see the language of the constitution as a whole being ignored or bastardized by this congress in just such a way as I questioned previously though.