You're creating a circular argument, one that does not exist. The presumption is validity, not invalidity. All the cardinals who voted in the conclave accepted his election, and we must also. No matter the "proof," it is an exercise in futility to attempt to prove invalidity of any papal election.
The thinking in your first sentence above is altogether contrary to the belief that binds us as regards the Church's indefectibility. I mean, Christ's promise is the Divine Revelation that tells us in no uncertain terms that the gates of hell will not prevail. So as far as that goes, the Church's indefectibility, being foundational, is not only not any concern of ours, it is our, well, our foundation that without, everything has already crumbled and hell prevailed.
The correct thinking is in knowing with certainty of faith that the Gates of hell will not prevail no matter what. Because we are absolutely certain of this we must also be certain that even *with* evil, apostate, heretic popes sitting in the Chair till, God forbid, the end of time, the gates of hell will still not prevail.
Just because a 'majority' accept something does not make it so, the truth is not subject to majority rules, especially in light of new information.
Absolutely certain of what exactly? Many other Christians say the same thing but are all so vague about 'the gates of hell prevailing' that it's rendered entirely meaningless. Yea we can be absolutely sure of something that cannot be clearly defined by anyone apparently.
Christ said this in relation to making St Peter the rock, the New High Priest of the New Covenant... the New Aaron in a single line of succession... now they sure made a mess of it with the Old Covenant too with Annas and Caiaphas etc, why did they bring Christ to Annas first (who didn't pronounce judgement) if Caiaphas were the legitimate High Priest.
So while it's quite messy trying to work it all out, we do have a legitimate High Priest of the New Covenant (Pope) who we pray for and owe allegiance to when it comes to ex cathedra. I can't pick and choose anymore than you can, which is why I can't just write them all off because I dislike and don't trust much of what went on around Vatican II... it's only Bergoglio I can do so because I have solid grounds for rejecting Pope Benedict XVI's faux 'resignation' and that faux election... therefore when I say such things it doesn't matter who Bergoglio is or what he has done... his heresies are merely a bonus that point to something being seriously wrong and looking further into it precisely because the gates of hell should never prevail.
With such vague explanations of 'the gates of hell prevailing' then IMO a Pope can literally do and say anything they want as there is then no such thing as a line in the sand or point of no return. Remember, this was given in direct relation to St Peter who is the High Priest of the New Covenant... the new Aaron of the Old Covenant, also why St Peter was with Christ during the transfiguration where God the Father said "This is my beloved son, in whom I am well pleased, hear ye Him" whereas Aaron was with Moses when he was transfigured coming from Mount Sinai where he received the Ten Commandments. Christ being the New Moses and St Peter being the New Aaron.
God Bless