Hi Matthew,
I am happy to answer your questions. Sedevacantism, when properly understood is logical, consistent and is thoroughly Catholic. As there are so many questions I will answer them in several posts.
* Does the Catholic Church have a pope right now?
* For how long has the commonly-held pope (in Rome) not been the real pope
1. No, the Catholic Church most certainly does not have a Pope. This can be proved in two ways. The antipopes are public heretics, as they are public heretics, they have lost their membership in the Church, and with that any office that they held.
2. Pope Pius XII was a certain Pope. The trouble begins during the time of John XXIII, but, I do not believe a strong case can be made against him. He was not a public heretic. Paul VI taught public heresy to the Church on December 7, 1965. I believe this date is a certain line in the sand. Whether or not Paul VI was a Pope or not prior to that point, he could not have been a pope from that day forward.
To answer your question, a future Pope may determine the date of sedevacante, we need only be concerned with what we can determine with moral certainty. We need not go beyond that.
We can have moral certainty that these claimants are not Popes, as they have taught public heresy, they have taught grave errors against the Faith, they have given evil universal laws, they have promulgated evil and impious sacramental rites. If they were Popes, the Church would have defected. The Church would lack Apostolicity in its Doctrine. The Church would also no longer be the guarantor of the Apostolic Succession, as Paul VI promulgated a doubtful rite. The Church would no longer be holy as its sacramental rites and laws have allowed evil and impiety.