All these traditions dictate that whoever the Roman Pontiff judges to be a schismatic for not expressly admitting and reverencing his power must stop calling himself Catholic. Since this does not please the neo-schismatics, they follow the example of heretics of more recent times. They argue that the sentence of schism and excommunication pronounced against them by the Archbishop of Tyana, the Apostolic Delegate in Constantinople, was unjust, and consequently void of strength and influence. They have claimed also that they are unable to accept the sentence because the faithful might desert to the heretics if deprived of their ministration. These novel arguments were wholly unknown and unheard of by the ancient Fathers of the Church. For "the whole Church throughout the world knows that the See of the blessed Apostle Peter has the right of loosing again what any pontiffs have bound, since this See possesses the right of judging the whole Church, and no one may judge its judgment." (Bl. Pius IX, Quartus Supra, 9-10)
Is this not a complete refutation of the SSPX position? Bl. Pius IX dismisses their argument for the injustice of the excommunication and for the state of necessity. Why? "no one may judge its judgment". Do you consider yourself included in that "no one", LOTI?
You just have: "I will grant you that the Tribunal attempted to excommunicate her; it would seem, however, that it was invalid (and hence there was no excommunication) since it was manifestly contrary to the law."
Get off the fence.
There is no presumption of validity when canon law is in contradiction with a papal letter. Papal law trumps a papal opinion expressed in a letter.