As usual, we have a very different understanding of that passage.
Again, the word you have used is a misrepresentation of Peter’s role as leader among equals. It is not a question of Peter’s being “superior” to the others or of them being subservient to him.
Jesus here is talking about His Kingdom and the difference between it and that of the Gentile kingdoms where the kings or the authority exercise lordship, or “lords” over them.
The Apostles were to be servants to the body of Christ.
That is why the pope is called the “Servant of the servants of Christ.”
Remember, the Apostles and the other disciples thought that Jesus was going to reestablish an earthly kingdom and that they would be the ones in charge.
Peter is the leader in so many situations in the NT, but no one has said that he was superior to the others.
Certainly not in the council in Jerusalem. James was the leader of that. Certainly not in Rome. Paul didn’t even mention him when writing to the Romans. Certainly not the night prior to Christ being deceived. Jesus told him to “get thee behind me Satan”. Certainly not when they took Jesus. Peter denied Christ three times.
No amount of proof will ever be sufficient but don't stop rebuking. To use a military term, this is a hill Protestants are willing to die for. Once they admit that Peter was the first Pope and that Catholic Apostolic Succession is proven their fig leaf is removed and they will have to stand before the world and their maker as naked heretics.
"For such is the will of God that by doing right you may silence the ignorance of foolish men." - 1 Peter 2:15