May I say you seem to be much more objective and reasonable than most, who seem to be easily trapped by fallacies and ipse dixit from their favourite personality/publication, often repeating verbatim arguments they don't appear to understand.
As if it would be more important to justify to others their own position/preference, more than determining the truth of the matter!
I will now however make some observations to your very well reasoned post.
No, LoT, Suarez can be rejected based on only a CERTAIN READING of cuм ex. Others have understood cuм ex quite differently. That's my point of contention.
Well, no, he can be rejected (in the sense of considered in error) by the same means Bellarmino et others did.
On top of that, it's not limited to cuм Ex, but all the Ecclesiology determined via several encyclicals since his time.
For instance the qualities of the Mystical Body, the Unity of Faith, etc.
It cannot be any other way without having to admit a non catholic could be elected as valid Pontiff. For instance a Jew could pose as Catholic and then be endowed by Christ as His Vicar.
Now, the canonical determination in the so called external forum is another matter.
ESTABLISHING the FACT of heresy is the big problem. If a Pope were to come out and say, "I know that the Church teaches [such-and-such dogma], but I refuse to believe it anyway." then clearly there's a case of manifest heresy in which deposition would have occurred without any further declaration. But what we have here is a series of Popes who apply some "hermeneutic of continuity", claiming that their doctrines are consistent with Tradition.
Really? The Remnant's position. You very well know that most heresies, and modernism in particular DO NOT directly reject any dogma but use subtle means of circuмventing and devoiding them of actual meaning.
So what you are saying is that more one closely follows the precepts and methodology of Modernism the less he is a heretic (or at least determinable as such).
With the added corollary of: the less a heretic is honest/stupid, the less he is one (or can be determine as such).
Most heretics claim their heresies are consistent with (their definition) of Tradition anyway.
But who then has the authority to tell a putative pope, "Uhm, no, that's heresy."?
Someone could try, but said papal claimant could just say, "Sorry, I disagree. Who are you to tell me that I'm being heretical?" That's where the missing ingredient is the authority of the Church.
Yes, that's why R&R makes no sense and can only be held by virtually sacrificing any prerogative of Pontiffs (and the Church herself at large, as it applies to most clergy anyway).
How the process would start is that various Catholics would start questioning and doubting the person's orthodoxy. Then the entire Church (likely through an Imperfect Council) would recognize such a one as alien to the Church and would repudiate him. Not that such a mechanism would EFFECT deposition. But it would be the recognition of this state. It's this recognition or lack thereof from the Church which establishes a priori the legitimacy or illegitimacy of a pope as dogmatic fact, and not the private judgment musings of any individual Catholics, regardless of how compelling an argument they think they can make for it.
But we KNOW nobody can judge a Pope. This is all speculation and very risky of Conciliarism. The elevation in itself cannot be reversed by a lower authority.
What can happen, and this is esplicitly said in cuм Ex. (which contrary to claims does not deal with depriving a Pontiff of authority) is the election being invalid in itself due to the candidate being outside the Church (heretic, schismatic, apostates, deviated from the Faith) without the Cardinals being aware of this at the time.
Where we stand today is in that stage where certain members of the Church are rightfully and reasonably and based on much serious postive evidence questioning legitimacy. But it MUST go beyond that before the SV conclusion can be reached. This private judgment must be confirmed by the Church. Until then it's only private judgment. In my position, this state of grave doubt suffices to render the papal claimants as "quarantined" (a very apt term introduced by Father Chazal), in a state where they are incapable of formally exercising Magisterium due to the doubt ("Papa dubius papa nullus.").
This is all well and good.. but let's be honest. It's not limited to Francis.
Deposing him (licitly or not, besides the point) could only ever give us another Modernist.
Francis is simply the expression of the most liberal and less orthodox wing of the NO. But can we point to even *one* single Cardinal who adheres to actual orthodoxy without a doubt?
This is why even some RRists now rely entirely for their hopes in DIVINE INTERVENTION (often linked to Fatima).
But we MUST defer to the Church and the Church's authority to make the ultimate determination (both formally and materially). Anything else absolutely DESTROYS the Magisterium no less than R&R does. In the meantime, these men continue to materially hold the papacy, and it is my opinion that those material juridical acts (such as appointing bishops) can still be exercised by a materially-legitimate pope even if he's formally lost authority. So if Francis appoints a bishop, and that bishop is not a heretic, then that bishop can formally exercise authority.
First off this ignores the very reasonable and possible fact that the NO ordination is invalid.. which would make the entire thing pointless and beyond redemption anyway.
Secondly, no, SV intended as a passive "precautionary" reaction from the faithful to a danger avoids all this.
Also the G.A... it is simply absurd (and faith destroying) to hold that this 60 year long, and universal, apostasy is simply a one-time aleatory accident with no repercussion or meaning beyond itself.
As I say and hold, this being "ordinary administration" and not an exceptional, divinely allowed, eschatologically crucial, part of End Times, would make Catholicism yet another false cult.
You CANNOT recover from this. For ever there will be doubt (and rightly so!) about what is actually true and orthodox and what could be a novelty.
Obedience and faith in the Pontiff (and your bishop etc.)would be a perpetual danger forever and you'd have to rely on private judgement and interpretation for all things Catholic.
A dead faith.