As to why Cardinal Siri did not publically support Lefebvre, I think this interview sheds some light on the subject. The last paragraph is key...
"No doubt, but he realized he could not go forward because this matter was not understood even by the traditionalists. It seemed to them that the whole controversy concerned the Latin Mass and the real problem was linked to the eighth commandment, the truth. Once again, the Cardinal was right and, above all, he had seen far away. He understood that in the logic of the left there is no being, no sense of reality, and that the ideology, the Cartesian cogito, is totally subjective."
To me it seems that Siri knew that the real problem was the lack of truth, or more exactly the loss of peoples ability to discern truth. Perhaps the destruction of the mass is not the central issue but rather the fruit of the general decline that started 800 years ago. Furthermore, Siri saw that the errors of V2, the new mass, etc. would not become obvious until well after his death.
2006 interview with Peppino Orlando of Genoa, religious writer and long time friend of Cardinal Siri
"My meeting with Cardinal Siri was at the Citadel, the Pro Civitate of Assisi, where I studied theology for three and a half years, from '58 to '61. Two retreats were dictated to the volunteers by the Cardinal. In this little chapel where we met, Siri was revealed for what he really was: a man of faith, a theologian and man of culture, trying to understand what made a genuine spiritual formation. I was very impressed by these encounters to the point that I asked for an interview with him. The first question he answered, I still remember, it was this. "Your Eminence, I said, what is the key thing that those who want to Christian culture must have?" I figured he would pull out, for example, the Bible. But, he said, ontology, logic and ontology. Without those you cannot possibly go to the Bible, which is the subject of Logos. "Remember, Orlando” - I still remember the words with which he concluded his speech – “that where there is no logic, grace cannot take root." Not surprisingly, modern philosophy, Kant, Hegel and Marx, attacked logic and ontology, indeed, first they attacked the ontology and then the logic.
"Today you are convinced of the validity of this teaching?"
Absolutely . I have remained faithful to this speech. For me, philosophy, spirituality and theology must always be together. Indeed, despite the chaos in which at some point I dived, namely participation Catholic dissent, this was the lifeboat that brought me out of the left.
"What had Siri observed of the world of the left?”
"Without doubt, the illogicalness and the lack of sense of being and of reality. That sense of reality, however, the Cardinal possessed as did the president of Confindustria at the time, Angelo Costa, who I am connected by marriage. Economics, yes, but after the economy the ten commandments. In fact, I often wondered why Siri insisted so much on the eighth. Do not bear false witness.
"Did you get an explanation?"
Certainly. The cardinal wanted to emphasize the absolute value of truth. Another of those values which formed a kind of red thread throughout my life. And this was noticed by my old master of Assisi, which, who, despite my position of leftist dissent of those years, had given orders that I be received in the archbishopric. I remember the discontent of many priests and monsignors, being passed up for an interview with Siri. And I also remember the "grumbles" for example, that His Eminence received more enemies than ever faithful servants of the Church. But anyhow. For me there was always free passage.
"And what were you talking about in those meetings?"
The Church, the contentions. Friendship with Siri gave me those counter-poisons that, in the long run, would allow me to get out of the left itself. Just that - and that Siri had well understood - the Church of that time and, unfortunately, which today lacks the pope. The Pope is not only the bishop of Rome, but he who holds the authority of government and education, and that strengthens the faith of his brothers. The Council and Paul VI, however, refused the tiara, had somehow deprived the pope of the power of jurisdiction. In short, we have moved from the monarchical principle of Peter in this collegiality, which is based on opinion only.
“Siri therefore had perceived the danger of a loss of the infallible authority of the pope?”
No doubt, but he realized he could not go forward because this matter was not understood even by the traditionalists. It seemed to them that the whole controversy concerned the Latin Mass and the real problem was linked to the eighth commandment, the truth. Once again, the Cardinal was right and, above all, he had seen far away. He understood that in the logic of the left there is no being, no sense of reality, and that the ideology, the Cartesian cogito, is totally subjective."