So +Schneider opens by rejecting +Vigano's vitium consensus position, calling it "extremely weak".  He claims that analogy with intention to receive a Sacrament doesn't apply, because we're dealing here with an office rather than a Sacrament.  This is a gratuitous assertion that is not backed up by anything, and it's false.  This is an analogy for sure, and analogies aren't perfect, but there's sufficient similarity between the two to justify the analogy.

Both the reception of a Sacrament and assuming the papal office require consent.  If a man were elected pope and did not give his consent, he would not be the pope.  So the analogy is quite valid.  Question is WHAT the individual needs to consent to, merely to have the title?

He also claims that intention is a matter of the internal forum.  This too is completely false.  Intention is something that can be expressed and known in the external forum.  "Internal Forum" only applies to matters related to subjective guilt and subjective dispositions, but things like intention can be known in the external forum.  If a woman told some friends that she intended to marry some guy just to get his money and had every intention of divorcing him after a few months, walking away with child support and alimony, that intention has been manifested in the external forum.  Now, her degree of guilt, given her knowledge, etc., THOSE are matters for the internal forum, but intention can be known in the external forum.  +Vigano makes a case for why we can know from the external forum that Bergoglio intended to "change" the Church ... based on his own public statements, and since the office of the Papacy inherently (as taught by Vatican II) is to preserve and safeguard the Deposit of Revelation (for which +Strickland even called out Jorge for denying), the argument is that he did not mean to assume the papal office in terms of what its purpose or primary end was.

+Schneider then tries to make a false analogy with popes who only accepted the office for ulterior motives ... so they could enrich themselves, etc. and didn't really care about the papacy.  But none of these pervert popes expressed any contrary intention regarding the papal office itself, that they wanted to use it to change and corrupt the Church.  They simply had ulterior motives.  I liken this to the ends of marriage.  Most couples make use of that without any explicit thought or regard for the primary ends of marital relations, the procreation of children.  But so long as they don't exclude the primary end and recognize it intellectually to be the primary end, they're not subverting or excluding the primary end of marital relations.  Same thing with these popes.  They were primarily motivated by the ancillary benefits of being the pope, but they did not exclude the primary end of the office, to safeguard the Deposit of Revelation ... even if they could hardly care less about it on a day to day basis.  Argument regarding Jorge is that he deliberately sought to exclude and to contradict the primary end of the papal office, namely, to safeguard the Deposit of Faith.

I'll come back to the rest later.

On the one hand, if Vigano is right, then all the adverse consequences of the sedevacantist position must now be dealt with (eg., the disappearance of apostolicity, and so on).

So in the next section he's denouncing the notion that any kind of irregularities in conclaves would render an election invalid, since once he's accepted by the Cardinals and Bishops, he's the pope

It's as if he's extrapolating a non-decision from the Magisterium as a decision that Popes cannot lose office on account of heresy.  There's an overwhelming consensus to the contrary since the time of St. Robert Bellarmine.  Even those who continue with the Cajetan / John of St. Thomas position don't agree with this.  It's utter nonsense.  Basically, he's pretending that the Magisterium has endorsed the "third opinion", which is utter nonsense.

He gets really ridiculous toward the end, when he's asked whether if a subsequent Pope were to retroactively declare Jorge a heretic and non-pope, he would fight that or accept it.  He says the Church will never do this because the Magisterium has never endorsed the idea that a Pope would lose his office for heresy.  So what?  Just because the Magisterium hasn't endorsed the idea yet (although we do have a teaching from Pope Innocent that says otherwise, and Paul IV says otherwise, etc.), the Magisterium hasn't rejected the notion or ruled it out.  It's as if he's extrapolating a non-decision from the Magisterium as a decision that Popes cannot lose office on account of heresy.  There's an overwhelming consensus to the contrary since the time of St. Robert Bellarmine.  Even those who continue with the Cajetan / John of St. Thomas position don't agree with this.  It's utter nonsense.  Basically, he's pretending that the Magisterium has endorsed the "third opinion", which is utter nonsense.