That's the million-dollar question and why many of us who accept sedevacantism here don't accept a totalist position. For example, I accept SV but hold to the Cassiciacuм/Fr. Chazal position (material/formal distinction) on how to address the current hierarchy. Meaning, if Francis, who only holds the material office of the Pope, were to suddenly convert and renounce the Council and all his errors he would then receive the formal office of the Pope. Which solves the problem of the hierarchy and Cardinals. 

Many who take a position where there are absolutely no valid Cardinals would either say that God will select a new Pope through Divine intervention, or that these are the last days and Antichrist is coming very soon.

Short answer: you don’t form theological position base on private revelation.

Galatians 1:8 “But though we, or an angel from heaven, preach a gospel to you besides that which we have preached to you, let him be anathema.”

Beside, these clowns have no power to do anything. If they can consecrate Russia, they can likewise “canonize” Karol Wojtyla. Personally I’m inclined to the Dimond Brothers’ explanation, that Pope Pius XII has consecrated Russia. Mock me if you will, whether it’s a “great deception” or not, I would still be glad that that monster got away for some time. At least in the Western world and in Russia today, you can on theory practice Catholicism publicly, a thing the Soviet Jєωs forbade.

No mockery here. I believe that Pope Pius XII consecrated Russia in 1952 as well. But some are holding out until 2029, due to comparisons to the consecration of France to the Sacred Heart, which occurred at the last hour 100 years after Our Lord's request to St. Margaret Mary. I'm not convinced, as the "errors of Russia" have so obviously spread. And Pius XII doing the consecration in '52, when the clergy and hierarchy was already full of Communist wolves, fits the bill.

The Sedeprivationism position seems to be the best solution. It basically states that the person occupying the role of Pope is indeed the valid head of the Vatican City state, but is not formally the Vicar of Christ. As head of that state, he has to perform the duties to maintain it such as appointing cardinals. All appointed cardinals are valid as the current "pope" has the authority to appoint them according to the laws of the state. Since the cardinals are valid, they then have the authority to elect the next head of the Vatican City state, whom, if validly elected and free from heresy would be a valid pope.

If say the current popes and Cardinals' etc did convert, what would that mean for their orders? Are are all of their orders not invalid or at best doubtful, as most, if not all of them received their Holy orders after Vatican II?

If say the current popes and Cardinals' etc did convert, what would that mean for their orders? Are are all of their orders not invalid or at best doubtful, as most, if not all of them received their Holy orders after Vatican II?

As we are speaking of a Divinely-instituted and -protected society, that will all be taken care of in the process.  God is a God of peace and does not want us to be overly worried about things above our proverbial pay-grade.  He is our Father and is as much in control of everything during this dark time as He was in the 13th century.  Hold fast; worry not.  Godspeed

Just to give an alternative, "totalist" perspective (in brief):

Cardinals are not necessary for an election.  This is because although it is part of the ecclesiastical law of the Church that cardinals have sole powers of election, this has been rendered impossible to follow because all of the validly appointed cardinals have died.  Thus, the power of election devolves to the wider Church.  This means a general council of bishops would suffice.  However, since the traditional clergy do not have jurisdiction in any real sense, they do not have the authority to elect a Pope.  This means there must be bishops who have ordinary jurisdiction who can have the potential to elect a Pope.  Contrary to the claims of some sedevacantists (and more anti-sedevacantists), we do not claim that there are no bishops with ordinary jurisdiction.  Instead, some believe that God supplies the jurisdiction to an antipope where there is invincible or common error for the good of the Church *to the extent necessary* e.g. to appoint true Catholics to an office (similar to the jurisdiction enjoyed by some invalidly appointed bishops during the GWS).  Thus, these bishops who enjoy ordinary jurisdiction must be present at any such election however it appears any known bishops of such stripe are unwilling to do so or are simply unknown to wider public (which I suspect is the case for various members of the Eastern clergy). 

Thus, the potency for an election exists but is unlikely to occur through natural means however this is a shared problem for all shades of traditionalism and not unique to sedevacantism and as such it is irrelevant to speculate how likely or unlikely such an election could ever occur.  As for our part, all that we can do as laymen is pray for our clergy and pray for an end to this crisis.

Just to give an alternative, "totalist" perspective (in brief):

Cardinals are not necessary for an election.  This is because although it is part of the ecclesiastical law of the Church that cardinals have sole powers of election, this has been rendered impossible to follow because all of the validly appointed cardinals have died.  Thus, the power of election devolves to the wider Church.  This means a general council of bishops would suffice.  However, since the traditional clergy do not have jurisdiction in any real sense, they do not have the authority to elect a Pope.  This means there must be bishops who have ordinary jurisdiction who can have the potential to elect a Pope.  Contrary to the claims of some sedevacantists (and more anti-sedevacantists), we do not claim that there are no bishops with ordinary jurisdiction.  Instead, some believe that God supplies the jurisdiction to an antipope where there is invincible or common error for the good of the Church *to the extent necessary* e.g. to appoint true Catholics to an office (similar to the jurisdiction enjoyed by some invalidly appointed bishops during the GWS).  Thus, these bishops who enjoy ordinary jurisdiction must be present at any such election however it appears any known bishops of such stripe are unwilling to do so or are simply unknown to wider public (which I suspect is the case for various members of the Eastern clergy).

Thus, the potency for an election exists but is unlikely to occur through natural means however this is a shared problem for all shades of traditionalism and not unique to sedevacantism and as such it is irrelevant to speculate how likely or unlikely such an election could ever occur.  As for our part, all that we can do as laymen is pray for our clergy and pray for an end to this crisis.

This is my position, too.