While Paul was a great write and Apostle, and is mentioned many times in Papal Decrees and Encyclicals as being also the one who Popes succeed, being his successor has no real effect other than prestige. All bishops are successors of Apostles- it matters to be successor to Peter in Petrine ministry, not in Apostolic ministry. Every bishop can claim to be (in some sense) successor to any (or all) Apostles (including Peter) in their Apostolic ministry and full powers of priesthood. However, only Bishop of Rome can claim to be successor of Peter in sense of Petrine Ministry (and being Rock of the Church).
If Second Ecumenical Council recognized by Pope (so not the canon concerning Constantinople superceding other Patriarchs and being equal to Rome) recognizes St. Andrew as having formed Byzantium, it is clearly truth as Holy Spirit who leads Ecumenical Councils can not lie. If not, however, it is left to historical interpretation.