I have a couple of questions for you all.
V & W, leaving aside the whole Babylon thing, it is demonstrable that from at least about 100 AD Christians believed that both +Peter and +Paul were at Rome. Thereafter the testimony of The Fathers as well as the bishops of The Church is uniform that +Peter was at Rome. Was there ever a time when anyone in The Church denied what The Church always and everywhere believed (and indeed prayed in its Kontakia, Troparia and Apolytikia) concerning +Peter's presence in Rome or that the bishops of Rome are the successors to +Peter?
And to you, M, why does it make a tinker's dam of difference to you, who apparently are neither Orthodox nor Eastern nor Roman Catholic, whether or not +Peter was at Rome? Certainly his location has no impact on the Apostolic succession of the bishops of Rome or on the traditional and canonical status of the See of Rome as the senior church in The Church, so I am at a bit of a loss as to your point.
Every credible source has always said that he was martyred in Rome.
"And to you, M, why does it make a tinker's dam of difference to you, who apparently are neither Orthodox nor Eastern nor Roman Catholic, whether or not +Peter was at Rome?"
Because it may to God's word.
You wrote: "Was there ever a time when anyone in The Church denied ....+Peter's presence in Rome or that the bishops of Rome are the successors to +Peter?"
Not that I know of off hand. There may have been some heretics (heretics for other reasons really) who did so.