I see. Anything that was written by the Church Fathers that supports your arguments is to be accepted as, well, gospel, and anything which doesn't is myth.
It takes more than a shovel to operate a cemetary. And wondering about the age of various cemetaries does nothing to make the point.
Yes, there was a small Jewish community in Rome, but remember that Paul was arrested immediately after entering Rome, that he spent his time preaching and converting as many as he could. Christians were being killed outright. Paul wouldn't have been considered a religious Jew at that point and Peter would not have been either. Remember too, that the Jews that were there wanted him arrested.
Therefore: no burial would have been available for Peter at a Jewish cemetary. Christians didn't have any. He had to have been buried in a pagan cemetary. QED.
So then where would Paul and all the other Christians who died there in Rome have been buried? pagan cemeteries too?