It is interesting John 23 named himself after the last anti-Pope and he didn't know what he was doing? He even moved a statue of the anti-Pope to a prominent place. This seems to coincide with your theory. Also all the things Paul 6 did, abolishing he oath against modernism and renouncing the tiara as the tip of the iceburg.
There are many data points that lead me to believe that this is the case.
It's well know that the Masons have been trying to infiltrate the Church for years; they have published their plans along those lines.
Bella Dodd admitted that the Communists had been systematically infiltrating the Church.
John XXIII's fraternization with Communists are legendary, and there are credible allegations that he joined the Masons. In one of his early encyclicals he wrote of a "mysterious force" rising in the world, with mysterious force being the original name for Fɾҽҽmαsσɳɾყ. One of the first things he did was to start brokering deals with the Communists so that they would let Orthodox observers attend V2. Masonic and Communist publications hailed his election.
Paul VI appears to be descended from rabbis on his father's side. He walked around wearing the ʝʊdɛօ-Masonic ephod of Caiphas. There are credible allegations that he ratted out clandestine bishops and priests behind the Iron Curtain to the Communists. That's in addition to the other stuff you mentioned.
John Paul II was alleged to be a peace priest, a Communist collaborator. While other Polish bishops were kept under tight control or even under house arrest, he travelled the world giving lectures of phenomenology. His mother was of Jєωιѕн descent, and his best friends growing up were Jews. Jerzy Kluger, a Jew, was granted the first private audience by John Paul II after his election. John Paul II has some very public meetings with Bnai Brith.
And all of these guys have been photographed giving and receiving Masonic-looking handshakes.
There's just too much here NOT to suspect them of being infiltrators.
Our Lady of Good Success warned of the secret sect infiltrating the Church, and Padre Pio was convinced that the Masons had infiltrated high places in the Church.