Convincing anyone that Peter was more then a chip of rock is only a small part of your problem, you still have to connect him to the Catholic church and Rome, so you had best get busy.:-)
Read Daniel. Christ hasn't fulfilled the prophesies regrding the overthrow of the fourth nation and the building of his church in it's place unless the Church is built in Rome. The apostles knew this and it shows why Rome was the focus of evangelism from the earliest days of the church (did you know that Rome was the only church that Paul wrote to when he had never been there? - just an aside).