Here's why I feel this is being muddled:
In a discretionary judgment, the Pope is not being judged per se, what is being ascertained, as Torquemada explains, is the truth of the proposition: "Jorge Bergoglio is no longer Catholic." So the Pope is not the object of this judgment, but rather, the proposition, "Jorge is not a Catholic."
This is NOT some kind of formal juridical thing, but rather, merely the Church coming to the knowledge and awareness of Jorge's non-Catholicity.
This requires no specific process, no declaration, of any kind. There are cases where the truth of the proposition would be just self-evident. "I, Jorge, have become a Buddhist" or "I, Jorge, don't believe in the Real Presence." No proceedings or declaration is required here.
It's in cases where there's disagreement or dispute or where Jorge adamantly denies the proposition that there needs to be a process of some kind, so that the Church might discern the truth of the matter.
We are not talking about any kind of LEGAL "conviction" where it comes to a discretionary judgment. "convinco" can have that technical legal term, but it is not so used when applied to a discretionary judgment. In that context it just means that the Church has come to be "convinced" that he's in fact a heretic.