I do not think the CHURCH was built upon PETER. Just as a practical Matter, reading ACTS, Paul and Barnabas and Mark and Timothy and Luke (traveling together and in pairs) spread the word and started more Churches (local congregations) than Peter did. I am not dissing on Peter, he was there, lifting and leading with the others (and having some firsts), but the bulk of the Church was built by Paul and his journeys. Even after the Apostolic age, most of what the church knows is due to the letters of Paul rather than Peter.
So if we set aside the PERSON (because history does not support that meaning), then what other possibilities are there?
Was the CHURCH built upon what PETER said?
Well, as you have actually pointed out quite well, the actual words of Peter were well timed, but not exactly a unique revelation. Peter was not even the first to say them (You quoted Nathaniel saying basically the same thing). However, I am a firm believer that CONTEXT IS KING and we would be fools to ignore what JESUS said ABOUT Peters words (which he did not say about any of the other times those words were spoken). "GOD REVEALED THEM TO YOU!" That is what Jesus said.
I posit, for your consideration, was that combination the ROCK (immovable bedrock) upon which the CHURCH would be built?
GOD would reveal the truth that "Jesus is the Christs, Son of the Living God" to those that would become the Church. and Peter (stone) was one of the first stones laid in the foundation of that CHURCH (along with the other Apostles that received that same revelation from the same source.)
So does the HISTORY of the church support that possible interpretation? Was the church built upon the "bedrock" of GOD revealing the Sov to those that would become the "Living Stones" in His Church?
You decide if the CHURCH was built upon a man, or upon a revelation of God. [I am unqualified to decide so important a matter for you.]