Nishant,
The teaching of St. Alphonsus, Cardinal Billot et al, are fallible teachings. There are numerous examples of Doctors of the Church holding conflicting opinions. Cornelius Lapide points this out throughout his commentaries. So if you are considering what S. Alphonsus said on this, why are you not giving weight to what S. Bellarmine, S. Francis de Sales, S. Antonius stated in support of sedevacantism?
Why overlook what the popes themselves wrote in support of sedevacantism? See Eugene IV, Council of Florence Cantate Domino, Pius XII Mystici Corporis Christi, Leo XIII Satis Cognitum, Innocent III Eius exemplo in addition to the Bull I've already provided by Paul IV. I didn't quote them because anyone who rejects sedevactanism in the 1917 Code of Canon Law and the Papal docuмents I've already provided, it seems to me is intransigent in their thinking.
Papal elections are not infallible. Pope Paul IV declared that infallibly in Bull cuм ex Apostolatus officio, which I provided to you in full. Read #6. Are you rejecting the excathedra declaration of a pope?
Furthermore, this has already happened, and it is widely accepted that the Cardinals elected an antipope. In the 12th century Anacletus II reigned 8 years in Rome while rivaling the true Pope, Innocent II. Anacletus was elected by the majority of the cardinals.
During the great Western Schism 15 of the 16 cardinals who elected Pope Urban VI withdrew from his obedience on the grounds that the unruly Roman mob made the election uncanonical. There was only one cardinal who did not repudiate Pope Urban VI, Cardinal Tebaldeschi, who died shortly thereafter leaving a situation where not one of the cardinals of the Catholic Church recognized the true Pope, Urban VI. All of the living cardinals then regarded his election as invalid.