How do you know Paul IV wasn't a heretic?
I mean considering some of the dubious actions he did, it seems that he falls under his own condemnations and nullifies his own decree.
From the Catholic Encyclopedia:
"Paul IV elevated to the cardinalate his nephew Carlo Caraffa, a man utterly unworthy and without any ecclesiastical training, and enriched other relatives with benefices and estates taken from those who favoured the Spaniards. At the end of the unfortunate war with Philip II the aged pope lost faith in his nephews and banished them from the Court. Still more disastrous were his relations with England, which had been reconciled to Rome by Mary, and Cardinal Pole. Paul IV refused to sanction Pole's settlement in regard to the confiscated goods of the Church, and demanded restitution. Pole himself was relieved by the pontiff of his legatine office and ordered to come to Rome to stand before the Inquisition. Upon the death of Mary and Pole, he rejected Elizabeth's claim to the crown, on the ground that she was of illegitimate birth. His activity was more fruitful in the spiritual concerns of the Church. He could boast that no day passed without seeing a new decree of reform. He made the Inquisition a powerful engine of government, and was no respector of persons. The great Cardinal Morone was brought before the tribunal on suspicion of heresy and committed to prison. Paul established the hierarchy in the Netherlands and in the Orient.
The pontificate of Paul IV was a great disappointment. He who at the beginning was honoured by a public statue, lived to see it thrown down and mutilated by the hostile populace. He was buried in St. Peter's 19 Aug., 1559, and was later transferred to S. Maria sopra Minerva."
I mean the whole point of Cum Ex Apostolatus Officio was to safeguard and guarantee the orthodoxy of the Shepherds.
By Fr. Cekada's standards as well, this Pope lost his office. So, appealing to it as a proof of sedevacantism is an exercise in circular logic. If it's accurate, he lost his office or never had it. If he lost his office, the document doesn't have force.
You could also argue since he was 83 years old in the year 1559 that he was not in control of his faculties when this document was promulgated.
The argument is not circular because you would first have to prove:
1) That what Pope Paul IV did was serious enough to amount to a loss of office...
2) That this loss of office took place before he promulgated the decree in question.