He would not make such denunciation it as ex cathedra infallible. Infallibility here is not really even relevant. A pope would simply not make pronouncement of faith and morals amid a controversy. He can't do it. He would put his infallibility into controversy within the Church were he to do that. If there is no unity with his bishops then he makes no infallible statement. After the heretics are excommunicated he, in union with the faithful bishops conceivably could. An infallible pronouncement also has to be of something that the faithful have always believed.
I agree that it is not a relevant question in the context of the thread.
I also agree that in all imaginable scenarios the pope would reach to restore consensus rather than make infallible pronouncements amidst controversy.
However, the 1st Vatican Council unequivocally states:
such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable.FIRST VATICAN COUNCIL (1869-1870)
The "consent of the Church" is, of course, desirable, but it is not a necessary condition of papal infallibility.