So what was this one sinful act that started this whole mess? Your argument seems to rest entirely on this single event.
From a historical perspective it seems like a single event, but we really don't know what exactly happened between God an man. What we
need to know is in the Bible, but as you are aware it does not explain things in great philosophical detail. The Jewish Kabbalists tried to do it, and it might be interesting to see how they interpreted the events...
But I digress, this 'sinful' act has long since ceased to be a single event - if it ever was. The way I try to understand it myself, is through the idea of 'knowledge'. Once you have gained knowledge about something - to 'know' it - it is impossible to 'unknow' it. If you read the story of Adam and Eve you get to know sin as a process of temptation-->contemplation-->disobedience to God (the act of sin) -->dishonesty-->shame-->guilt--> punishment etc.
What the Bible shows is just how potential energy changed into kinetic energy leading away from God. (A creation where potential wasn't possible would be a falsity. God did not create false freedom.) Whatever "happened", the result was that more than just our own 'state of equilibrium' was upset by this, and a veritable Pandora's Box was opened.
God constantly interrupts this process. He wants us to take responsibility for every step we take in any direction (this is why Jesus could say: just looking at a woman lustfully is already an act of adultery). When Jesus did miracles of healing and changing, he was showing is authority and power to interrupt this process and restore things - but it is significant that time and again he said something like "your
faith has healed you". He made it clear that the restoration or change still did not take override our freedom, but required a certain choice - a "siding with God". It requires the willingness to oppose the process and natural downward spiral of sin.
On that note, whatever "church" or "representation" of God we have here on earth, whatever message anybody brings or proposes to do - it should reflect this redemption that God envisioned. The concept that best reflects this is love. Whatever else we do, it should be aimed at restoring love and peace - to work against the negative kinetic energy unleashed by disobedience from God. Many spiritual religions realize this - that somehow harmony needs to be restored, that some kind of justice needs to be served, and that, somehow, death represents this disharmony - and because this is true, many religions also "ring" true.
But if any person, people or institution does not permit God to set the rules of this redemption, they are still caught up in this spiral of disobedience. The imperfect cannot become perfect by its own
because of its imperfection. The mortal cannot become immortal on its own, because it is by
nature mortal. This is the essence of the rift between us and God.
When the pope does God's will, he is indeed an instrument and representative of God - when he doesn't, he isn't. When any of us do God's will, we are representatives of Him. It was always God who showed mercy and wanted to bridge the rift. He chose one man to embody victory of death. In Christ, God's mission and man's situation were both crystallized. Through Jesus, God presented us with the Catalyst for His plan of salvation from sin - God's Spirit. The bridge has been layed, but the crossing is hard. God did not take away the world of suffering, or take us out of the world, He
crossed it (pun intended). Through Jesus, God provided and immortal body as a vessel for our (own) crossing. We must "clothe ourselves with Him". Through the Spirit, God also armoured us against spiritual onslaught. These things are hard to understand because they aren't measurable, scientific or neatly explained in some book.
Some people have died, or "fallen asleep" and are waiting on the other side of the bridge, the side that is immortal and timeless (whether they are in "purgatory" or not is irrelevant). Most people venture onto the bridge and become confused between the spiritual and physical world, because they do not take Jesus' hand and let Him lead. Most people forget who built the bridge in the first place, or Some envision multiple bridges and ways of crossing them, or an endless bridge, or some variation.
Where the body leads, the spirit will follow. Where the spirit leads, the body will follow. Faith or works? Both and neither. Salvation comes first from God, also by a 'single event' - the resurrection of Jesus Christ - but as with sin, this has become a process, a road we must walk in one direction or another.