So ... you've just admitted that you're begging the question.

Only because the question has already been answered above to the satisfaction of most reasonable people.  I beg it here to put Bellator back on track (he was on the verge of losing sight of that central premise of this thread).

“The great schism of the West suggests to me a reflection which I take the liberty of expressing here.  If this schism had not occurred, the hypothesis of such a thing happening would appear to many chimerical. They would say it could not be; God would not permit the Church to come into so unhappy a situation. Heresies might spring up and spread and last painfully long, through the fault and to the perdition of their authors and abettors, to the great distress too of the faithful, increased by actual persecution in many places where the heretics were dominant.  But that the true Church should remain between thirty and forty years without a thoroughly ascertained Head, and representative of Christ on earth, this would not be. Yet it has been; and we have no guarantee that it will not be again, though we may fervently hope otherwise. What I would infer is, that we must not be too ready to pronounce on what God may permit.”

Fr. Edmund James O'Reilly S.J., 1882 The Relations of the Church to Society

But in the GWS, there was always a pope. 
 
It was merely disputed which claimant was the correct t one.

Likewise, nobody alleged universal disappearance of a juridical hierarchy.

Would Fr. O’Reilly come to the same conclusion, given today’s different circuмstances?

Particularly when there are ZERO competing claimants (ie., not merely uncertitude about which claimant is the correct one, but a situation in which it is alleged there has been no actual pope for 60+ years).

O’Reilly’s quote does not fit the current situation.

Come on Sean, you are really stretching it. His quote absolutely corresponds with today’s situation, especially this part: “we must not be too ready to pronounce on what God may permit.”

Bellator Dei posted the perfect quote: "Why are you fearful, O ye of little faith?" Matthew 8:26

The situation in the GWS is exactly the opposite of the situation alleged by sedes today:

2-3 claimants (with one of them being a true pope)

Vs

1 claimant (with no competing claimants) who is not a true pope.

Basically, it comes down to believing that the Church and the Pope can officially teach error and heresy and ultimately lead souls into Hell or having a nearly unprecedented interregnum, which doesn’t conflict with any doctrine. The former forces one to believe that the Church has contradicted Herself, which is impossible, and the later forces the faithful to trust in God’s Divine Providence.

Seriously Sean, think about it.

How does sedevacantism and a 61-year (and counting) interregnum, with no way to ever restore a hierarchy, remain compatible with the Church’s teaching that there will always be perpetual successors?

How does sedevacantism and a 61-year (and counting) interregnum, with no way to ever restore a hierarchy, remain compatible with the Church’s teaching that there will always be perpetual successors?

Sean there is absolutely no contradiction. You can’t find a single theologian who will say that an interregnum has a limited amount of time. Sorry, but you must concede this point. 

Sean there is absolutely no contradiction. You can’t find a single theologian who will say that an interregnum has a limited amount of time. Sorry, but you must concede this point.

Right.  What is the exact limit?  3 years (we've had this), 5 years, 7 years, 15 years, 32 years 7 months 6 days 4 hours 5 minutes 32 seconds?  No, there must be some other criterion rooted in principle and not an arbitrary time limit.  With the old ecclesia-vacantist argument, the response was that it was when no more bishops with ordinary jurisdiction remain.  Except that in ANY papal interregnum the bishops lose the ordinary means of receiving jurisdiction ... the papacy.  In those scenarios, Christ supplies the Church with jurisdiction directly (so say the theologians).  But there's no reason this cannot continue for a rather protracted period of time.

Now, I personally hold that Siri was likely Pope until his death in 1989 ... so the sedevacante period has only gone on 30 years.

There are plenty of ways to restore the hierarchy.  Catholic theologians have dealt with scenarios in which Rome was destroyed along with all the Cardinals and Roman clergy.  They maintained that an Imperfect Council could then elect a Pope.  Cardinalate is not of divine institution, and the Church can designate a Pope.

An imperfect council of (those you allege are) non-Catholics???

Right.  What is the exact limit?  3 years (we've had this), 5 years, 7 years, 15 years, 32 years 7 months 6 days 4 hours 5 minutes 32 seconds?  No, there must be some other criterion rooted in principle and not an arbitrary time limit.  With the old ecclesia-vacantist argument, the response was that it was when no more bishops with ordinary jurisdiction remain.  Except that in ANY papal interregnum the bishops lose the ordinary means of receiving jurisdiction ... the papacy.  In those scenarios, Christ supplies the Church with jurisdiction directly (so say the theologians).  But there's no reason this cannot continue for a rather protracted period of time.

Now, I personally hold that Siri was likely Pope until his death in 1989 ... so the sedevacante period has only gone on 30 years.

Siri baloney and delusions aside, what you should really be asaking yourself is, "How long can God allow the entire teaching authority to vanish from Earth without violating indefectability, perpetual successors, visibility, etc. etc?"

Andwer: Not one milisecond.