You admitted both elements, that there's a judgment about reality and then a decision by the Church. That's precisely where the formal and material aspects come in. Whether you want to admit it or not, there's a role for the Church to play ... or else any bozo could wake up one morning and claim that the See is vacant. That's the beauty of the Thesis (sedeprivationism), where it finds the balance between ipso facto deposition and the removal from office. That principle is already there in the teaching of Pope St. Celestine, as cited by St. Robert Bellarmine. Pope St. Celestine refers to Nestorius as 1) having lost his authority and 2) excommunicandus ... someone who SHOULD be excommunicated (but hasn't yet). Otherwise, at John of St. Thomas pointed out in developing his position, the Church could devolve into chaos.
My mention of matter and form is in reference to the man (matter) and the papal munus (form). With the FACT of public defection from the Faith, the two become separated and hence the man goes from having the papal munus to not having the papal munus. It is at this point in time that a Catholic is no longer under obligation to obey him. Later the Church makes a declaration that the FACT took place at such and such a time, and enforces the loss of office that already took place. Excommunication is simply the legal penal effect of the FACT and not the cause of the loss of office. Note that Canon 188.4 is NOT in the penal section of the 1917 Code.
With sufficient evidence, moral certitude is attained on the part of the individual regarding the FACT of public defection. The Church's eventual judgment does not make the FACT, but only ascertains that the FACT took place, and thereby make the judgment binding on all Catholics. Regardless, from the moment of the FACT of public defection, the man has no claim to the office whatsoever. That he remains in an apartment tagged with "pope" on his door, until the Church makes the declaration, is purely accidental.
P.S., I hold the First Opinion that a true pope cannot become a formal heretic, occultly or publicly.