If he wasn't orthodox, then he would fall from the papacy anyway, which is what Br. Peter, and myself, suggested by his adherence to Paul VI as a valid Pope and celebration of the New Mass. That does prove he was no longer a valid Pope, per the arguments proffered by sedevacantism.
The problem with this line of thinking is it's too simplistic.
1. A pope's personal orthodoxy doesn't affect his office. Siri never tried to "teach" heresy as pope, so he couldn't "fall from the papacy".
2. It seems that Siri never considered himself the pope, so his "adherence" (I assume you mean recognition) of Paul VI would be similar to +ABL's recognition; that is, irrelevant.
3. Siri's celebration of the new mass has nothing to do with his papal office. He never imposed anything on the Church at large, so, again, his personal sins don't remove him from office.
Benedict XV, Pius XI, and Pius XII were many things, even weak, but they were certainly orthodox, they did not deny any dogma of the Catholic faith. The same cannot be said of anyone who openly accepts Vatican II and the "authentic magisterium" of the post-conciliar Antipopes.
Arguably, anyone who rejects Pius XII's Holy Week changes (most sedes) are implicitly arguing that such changes are unorthodox. Logically, if Pius XII issued unorthodox rites, then he would also be a heretic and lose office (according to sede logic). If Siri's saying of the new mass = heresy and loss of office. How can Pius XII keep his office after issuing the Holy Week updates?
False expectations are the entire problem I have here with this thesis beyond the fact that he may have been elected in 1958 and/or 1963. This divining what motivated him to stay quiet and accept the Antipopes and false teachings of the Conciliarists, when, as Br. Peter stated, Siri's "big secret" may have been as simple as him misunderstanding that he doesn't need to remain quiet about an invalid election.
Br Peter's analysis seems complex only because he assumes that Siri's later actions retroactively affect the 58 and 63 elections. This is similar to protestant errors of logic where they argue that "acceptance of Christ" = salvation but...if person X doesn't live a Christian life, then that's proof that he "didn't really accept Christ". So it's the logical error of "future proves the past". That's not the way the Church works.
Siri gets elected, he accepts, he is threatened, he resigns (under duress, so it's an invalid resignation). Siri continues on as a Cardinal, incorrectly assuming his resignation and silence are legal and binding. Maybe as years go by, he realizes he's wrong and his election to the papacy was true. Maybe he ignores his conscience and his friends, and continues on as a Cardinal (because he's scared of the threats). In this case, he's a coward, but he's still the pope. So God allows his sin of cowardness to = acceptance of V2 and the new mass (9+ years after his election) due to loss of grace.
You can't say that Siri's acceptance of the new mass in 1970 invalidated his elections in 58 and 63. That's totally illogical. The future does not prove the past. Was he elected in 58 and 63? Yes or no? What happened after is a mystery of grace and salvation and sin but has no effect on the papal election. To argue otherwise is retarded.