Do you hold the Material-Formal Thesis? 

It is a rare find it would seem. 

I don't think it's all that rare.

I believe that the formal/material distinction is quite real, and demonstrably real ... though one might argue about the details regarding its implications.  I don't like referring to it as "the Thesis" (giving the impression that it's nothing more than someone's pet theory) nor really the concept of "holding" it.  I believe it's a theory that makes perfect sense, rooted in a very real distinction between the material designation to office and its formal exercise.

Now, that's in theory ... but in practice I don't believe that any of the papal claimants after Pius XII were even material popes because IMO Cardinal Siri had been legitimately elected but then uncanonically and invalidly pushed out under duress, rendering his resignation invalid so that all the subsequent "elections" until his death in 1989 were therefore also invalid (e.g. those of Roncali, Montini, Luciani, and Wojtyla).  Since these were not even material popes, they couldn't even appoint legitimate Cardinals (except possibly by "Color of Title" ... though that's very uncertain), and Ratzinger was also quite possibly not a valid bishop (the first consecrated in the probably-invalid new Rite of Episcopal Consecration), and the same holds of Bergoglio (who may also not even be a valid priest).

So currently, I guess, Elwin and I have arried to the same point, of holding that Bergoglio is neither formal nor material pope, while finding the theory behind that distinction to be very probable, and practically certain.

I voted yes although with reservations. It doesn’t have historical support, so I believe it’s certainly not dogma, but offers a middle ground between strict R&R and dogmatic sedevacantism. Concerning the pope problem, I firmly believe no man has “the answer.” I have a high degree of respect for Bp. Sanborn and have learned a lot from his sermons and classes online. 

So, what Fr. Jenkins articulates as the driving force behind sedeprivationism isn't quite accurate.  It doesn't have anything to do with the Church being "finished" if there are no Cardinals.  Everyone's famliar with how St. Robert Bellarmine addressed the issue and concluded that even if they were all wiped out, the Church would never be left without a means to elect a pope, since the Cardinalate is not of Divine Institution.

There's no denying the formal / material aspects in the election of a pope.  When the Cardinals elect a pope, unlike in Democratic theory, they do NOT thereby endow the man with some kind of authority, as if the authority comes from below, from the people, from the (consent of the) governed.  When they elect an individual they merely DESIGNATE the one they have chosen for GOD to then imbue with the authority.  So what they do is to materially designate him for authority, whereas God provides the formal authority.

Cardinals could designate an individual all they want, but until they accept there's no papal authority there (thus the principle behind +Vigano's vitium consensus theory).  If the Cardinals were to elect a non-Catholic, say an Orthodox bishop (and we're not too far away from this with the Novus Ordo), they could elect him all they want but that individual would not be capable of formally receiving the divinely-communicated authority.  Or if the Cardinals elect some guy they thought was alive (though not there) but who had actually dropped dead hours before, etc.  If the Cardinals elect a simple priest, and he accepts, he'd get SOME of the papal authority right away (ability to make appointments, etc.) but he couldn't exercise the plenitude of papal authority (e.g. teaching) without becoming part of the "Teaching Church", and only bishops are part of Teaching Church and can teach with authority.  If he continued to persist in refusing consecration, that would be construed as a tacit resignation (or even non-acceptance, again per vitium consensus).  By refusing to accept being a "Bishop", he's effectively refusing to become Bishop of Rome and therefore Pope.

These are just a few examples that speak to the distinction between the (material) designation to office and the formal exercise of said authority, so there's a very real basis in theology and philosophy for it.  It's analogous IMO to the ratum sed non consummatum distinction with marriages, where until the marriage is consummated (and the couple formally united), the marriage can be dissolved.  Similarly, if the Cardinals elect some guy, decide 5 minutes later that he's a heretic, they can immediately "withdraw" the designation for this same reason, or later on down the road if were to fall into heresy, they can withdraw the designation since the individual could no longer exercise formal authority, and the Pope is by definition the Bishop of Rome.

So these distinctions are very real and one cannot actually understand the Catholic theology of the papacy and papal election without them.

Now, there are some disputes, where the Cajetan school for instance hold that heresy does not deprive a pope of formal authority until the material designation is withdrawan by the Church (seriously problematic and since VI probably also heretical), and then if a Pope were to lose formal authority by heresy, and yet he did not lose his designation to office, what state is he in then?  Can he still appoint bishops or Cardinals or act as a conduit for jurisdiction?  Well, even the sedevacantists think it could be possible due to "color of title" ... which actually might speak to the same thing but without the clarity of scholastic distinctions.

Simlarly, let's say you have a bishop who's become a flaming heretic.  Until Rome intervenes to remove him, can he continue to provide jurisdiction to his priests, say, for Confessions, or appoint priests to be pastors of individual parishes, etc.  I would think so.  It's quite clear that Cushing was a manifest heretic by sedevacantist standards ... but even if you disagree, let's assume he was for the sake of argument.  Since Rome didn't remove him, did he stop being able to appoint priests to parishes or conferring jurisdiction for Confession (acting as a "condiut" for the jurisdiction via the Pope)?  Of course not.  So this is the same state that privationists consider heretical popes to be in.

Now that we've established the reasonableness of sedeprivationism (Bishop Dolan's claim that it's borderline heretical ... is just utter nonsense).  Oh, and notice that Fr. Jenkins calls him Fr. Dolan and also Fr. Sanborn, not bishop.  Back to the point, now that we've established the reasonableness of sedeprivationism, the actual problem this addresses is not, as Fr. Jenkins stated, because the Church would be "finished" without Cardinals (it wouldn't be), but the problem that the Church's authority MUST have some involvement in ascertaining (criteriologically, quoad nos) the reality of papal authority (quoad se), or what I would call the "Aunt Helen" problem.  If Fr. Cekada's infamous Aunt Helen were to have been alive during the reign of Pope Pius XII, if she just woke up one morning and decided that Pius XII was a heretic (say on account of NFP, evolution, or something else), could Aunt Helen just declare the Holy See vacant and start acting as if that were true, setting up her own chapel and inviting some suspended priests to offer the Sacraments there?  Of course not.

I myself was turned back from dogmatic SVism (and I owe this man a debt of gratitude) ... when I was with then-Fr. Sanborn and to the right of him on some issues ... when this man came up to me and told me that Pius IX had been an Antipope based on some "heresy" he had discovered in one of his encyclicals.  I thought to myself ... so where's the principled "backstop" to the chaos that would result if we said that any Aunt Helen could just conclude this?  There is none in straight SVism, nothing to prevent this runaway ad absurdum problem.  I had no solution to the conundrum, but R&R wasn't the answer ... so I remained in a state of suspension for some years, until I arrived at my own version of sedeprivationism (I had never really studied the "Thesis" but had just heard about it).  Ironically, years later, Bishop Sanborn and I ended up both arriving at the same place, on totally independent and different journeys ... at sedeprivationism, a theory which is not only rooted in well-established Catholic theology (material vs. formal aspects of papal election) but also finds a balance between ipso facto deposition that must be the case for reasons explained by St. Robert Bellarmine and the role of the Church's authority (vs. any rogue Trad armchair theologian deposing popes) ... namely, sedeprivationism.  Nothing else makes a lick of sense.