What is the "validity of the Catholic understanding of the Sacraments?" That they are believed to take place, mystically, and ineffably? How rational is that?
I can do so based on indisputable facts that certain verses happen to be in the scripture we all (maybe you being an exception) consider God-breathed and inerrant, and on facts of history
Then it's not based on reason, but on faith that what is in scriptures is God-breathed and true. Faith is not reason; it is used as the reason for praxis. And historical reasons do not make sacramental rituals "valid." History provides valid insights into when such practices began and for what reason, but history by itself does not validate the reasons offered for understanding of sacraments. It merely makes them manifest.
I don’t think you understand the distinctions between faith and reason that I made in my post.