Ok, excellent.
It's always interesting to read the rather ingenious theories both John Lane and John Daly try to come up with to save sedevacantism, both in trying to blunt the force of the argument and in trying to turn it on SSPXers and non-sedevacantists! It's a good attempt, but I think it falls short.
Against these, though, two points may be noted, which are both alike easily proved from authority.
First, that universal consent given to such and such a person as head of the universal Church and the one to whom supreme jurisdiction has passed in act is not something more or less imperceptible or requires great delay to be certain of but is in fact immediately recognizable as such.
Here is Msgr.Journet describing the same, referencing John of St.Thomas,
But the peaceful acceptance of the universal Church given to an elect as to a head to whom it submits is an act in which the Church engages herself and her fate. It is therefore an act in itself infallible and is immediately recognizable as such. (Consequently, and mediately, it will appear that all conditions prerequisite to the validity of the election have been fulfilled. )
Acceptance by the Church operates either negatively, when the election is not at once contested; or positively, when the election is first accepted by those present and then gradually by the rest (cf. John of St. Thomas, II-II, qq. 1-7; disp. 2, a. 2, nos. 1, 15, 28, 34, 40; pp. 228 et seq. ).
A simple nominal acceptance of his person as Pope, say in one's letters and speeches, or in one's private and public prayers for Pope Benedict XVI as Pope is enough for the same.
The second point, which it appears to me is even more devastating, is that this is a truth primarily received on magisterial authority - that is, it is declared by a moral unanimity among those bishops who belong to the episcopal college and have a teaching office in the Church. This is also mentioned in both the AER article and by Monsignor Noort when it is said for instance "The whole Church, teaching and believing, declares and believes this fact" in the former and "the ordinary and universal magisterium is giving an utterly clear-cut witness to the legitimacy of his succession” in the latter, to which declaration of the ordinary and universal magisterium dispersed throughout the world we give an assent of faith as to something infallibly true called ecclesiastical faith.
That's why I think the notion that we are in an interregnum is self-refuting - for assuming we were in one, then such a universal consent among Bishops that this individual - Benedict XVI - is the Pope would suffice to actually pass on to him the supreme jurisdiction by such an universal acceptance, and also to show infallibly that "all conditions prerequisite to the validity of the election have been fulfilled".
A few points:
1. I do not think we can put the post Vatican II popes in one basket here. There are differences between John XXIII, Paul VI, verse John Paul II and Benedict who I believe can be studied together.
2. I do not see it as any urgent situation to study John Paul I, as his time was short, and his actions as "pope," were not to bind Catholics to evil laws or or heresy.
3. So, I would like to focus my attention on the two latter claimants who I believe the case of a failure to universal acceptance is airtight.
4. At the time of the election of John Paul II, there was a growing sedevacantist movement that outright rejected his claim. Second, there was a very large body of Catholics who accepted him only in name as pope, but not in any Catholic sense as a pope.
The second group treated John Paul II and Benedict XVI as figureheads whose teaching and laws were rejected. Further, this group rejected the authority of the bishops in communion with these men.
Whatever way you want to slice it, your argument that using a man's name as pope, but not in anyway considering him as pope would have not in any age of the Church been regarded as a peaceful acceptance.
Did Catholics at the time of Pius XII's election, form numerous groups of independent chapels in opposition to his teaching, laws, and hierarchical structure? The idea of would have been preposterous. Catholics peacefully accepted Pius XII, and recognized him both in name as pope and in practice as pope, the man who took the office of St. Peter's successor, who would rule over all Catholics in spiritual matters.
5,. In addition to the many sedevacantist Catholics, and Catholics who used the name of John Paul and Benedict, but rejected their claims in practice, another group are those who remained under them, and to some extent accepted their laws, but rejected their teachings, especially on matters such as interfaith, ecuмenism, religious liberty, etc.
Catholics for the entire history of the Church have never accepted a pope, while maintaining the idea that they could reject him on matters of Faith or law.
6. The last body of those who accepted the claims of John Paul II and Benedict are by far the largest group, and these are those "catholics" who no longer believe what the Church teaches anyway on many subjects, such as contraception, interfaith, believing the Church's teaching, "no salvation outside the Church, that schismatics and heretics are in partial communion with the Church, believe that all men are saved and no one or almost no one goes to Hell, doubt or deny purgatory, and on and on the list could go. This body of people is very large, but their acceptance is not relevant, the group who is relevant are the Catholics who have kept the Faith.