WOW, I do not mean to be rude, but I remember when I had the same questions! lol.
Here is an even more fundamental reduction:
1. The 1968 rite of episcopal ordination is invalid due to a lack of form. Remember, a valid sacrament needs form, matter, and intent. If there is a deficiency in any of these three, there is no valid sacrament. In addition, according to Pope Leo XIII a sacrament must symbolize what it effects, and effect what it symbolizes. Now, the 1968 rite of episcopal ordination does NOT unequivocally convey the ORDER to which one is being ordained. It is not clear that one is being made a bishop in the prayer of consecration. Therefore, it is better to treat all Bishops ordained in this rite since 1968 as invalid, as well as ALL the priests that they have ever ordained.
2. This means that NO sacrament offered by any of these priests can be considered valid, with the exception of baptism, and possibly matrimony.
3. That also means that any cardinals who were made bishops after 1968 are most likely not valid Bsishops.
4. But Ratzinger was consecrated Bishop in the 70's!
5. Therefore, since his episcopate is gravely doubtful, his election and installation are extremely doubtful, for there can be NO Bishop of Rome who is not...a bishop. A Priest cannot be Pope. But tis is EXACTLY what Fr. Ratzinger is. a Simple Priest.
6. The Popes have no authority to alter the substance of the sacraments: But Paul VI sought to alter them: Therefore he is either not a true Pope de facto, or he lost the Papacy through the promulgation of a Council that redefined the nature of the Church which placed HIMSELF as the head of something NEW, which makes him other than...Pope.
You see the line of arguments here?
THere are about 4 more different arguments that can be made, including the Siri thesis, the public heresy/loss of office thesis, etc.
The odds are HORRIBLY against these last 5 "Popes", who have ALL taught heresy.