That's a different question again TTWSYF. I've some sympathy for the idea of Paul (with his claim of divine epiphany) presenting a challenge to what was previously run by those who claimed direct personal knowledge of Jesus. But that's not a church established in Jesus' lifetime. Other than Matthew, which is clearly not saying what you want it to, you haven't presented anything to show a church established in Jesus' lifetime. Your personal belief on how it started is one thing, proving it another. You've not made it past first hurdle on proving it even from the canon, and with someone who is letting you assume it is divinely inspired word relaying accurately historical events and not debating the translation of 'ekklesia' to 'church' as we both seem to understand it.
Just curious, but other than the canon bible, have you read anything at all written by early christians? Or even commentary which covers them? Honest questions. You referenced the church fathers, but must surely be aware that they don't agree amongst themselves over basic doctrine?
I'm an evidence driven man TTWYSF. Show me the evidence. Show me the explicit texts which say "Jesus began the church and then when he died Peter took over". Even the catholic church only claims its origins from after Jesus' death, and use the Peter/rock thing as proof of primacy amongst churches (plural) for Rome.