What we do know is that the Holy Spirit protects the papacy from doing this kind of serious damage to the Church. Bottom line, however, is that they cannot be legitimate Popes acting freely. That's contrary to the indefectibility of the Church.
What is the nature of the Holy Ghost's guidance of the Papacy? There are distinctions.
The pope is infallibly prevented from making an error when pronouncing a dogma 'ex cathedra'. In no other circuмstance is the pope infallible. Neither in personal morals, nor in sermons, speeches and letters.
Surely the Holy Ghost offers graces of state to the pope, but where is the doctrine that the pope cannot refuse these graces?
If these recent popes were pronouncing their errors as dogma, then we would have our proof. Note that they consistently refrain from doing this. Only John Paul II spoke 'ex cathedra', once (and even that can be argued!), to pronounce that no woman could ever be a priest.
We have no proof. We must behave according to the presumption that they are valid popes. Presumption!--not certainty.