[Tantumergo]

"The word "subsist" implies that there are other churches which make up what Vatican II calls the Church of Christ."

Your understanding of metaphysics is what is letting you down here!

Any particular body can only have one subsistence, therefore your implication that "subsist" implies that other churches make up "the Church of Christ" is quite incorrect.

To say that the Church Christ established subsists in the Catholic Church is also to say that it subsists nowhere else.

The word "subsist" does allow for the fact that lost sons and daughters of the Church exist outside her, as do elements of her life e.g. baptism by heretics and schismatics is still valid baptism which constitutes those who receive it members of the Catholic Church until they adhere to a heresy or commit a schismatic act.

[ultima ratio]

You are the one who apparently has a faulty understanding of these usages. "Subsist" was used instead of "is" precisely as a concession to other Christian churches, especially the Orthodox. It was meant to suggest--and does--that the Church of Christ exists elsewhere and is NOT identified solely with the Catholic Church. Only the verb "is" could establish such an absolute identity--which is the verb that had always been used by the Church in its preconciliar documents. By rejecting this term, the bishops broke radically with traditional Church doctrine and introduced a distinct and troubling novelty.