Just so we're clear, is your position that the See of Antioch is not occupied by the successor of St. Peter, and that therefore St. Evodius wasn't ordained by the Apostle as is accepted by both your church and the Orthodox? If that's your position then all that is necessary is to show that Evodius was ordained by Peter,
"You have been the disciples of Paul and Peter; do not lose what was committed to your trust. Keep in remembrance Euodias, your deservedly-blessed pastor, into whose hands the government over you was first entrusted by the apostles." - Pseudo-Ignatius to the Antiochians
"Peter the Apostle, by nation a Galilean, first high priest of the Christians, after he had been the first to found a church at Antioch, proceeded to Rome, where as bishop of the same city he remains, preaching the gospel for 25 years." - St. Jerome, Chronicle
"Now concerning those bishops which have been ordained in our lifetime, we let you know that they are these:— James the bishop of Jerusalem, the brother of our Lord; upon whose death the second was Simeon the son of Cleopas; after whom the third was Judas the son of James. Of Cæsarea of Palestine, the first was Zacchæus, who was once a publican; after whom was Cornelius, and the third Theophilus. Of Antioch, Euodius, ordained by me Peter; and Ignatius by Paul. Of Alexandria, Annianus was the first, ordained by Mark the evangelist; the second Avilius by Luke, who was also an evangelist. Of the church of Rome, Linus the son of Claudia was the first, ordained by Paul; and Clemens, after Linus' death, the second, ordained by me Peter. Of Ephesus, Timotheus, ordained by Paul; and John, by me John. Of Smyrna, Aristo the first; after whom Stratæas the son of Lois; and the third Aristo. Of Pergamus, Gaius. Of Philadelphia, Demetrius, by me. Of Cenchrea, Lucius, by Paul. Of Crete, Titus. Of Athens, Dionysius. Of Tripoli in Phœnicia, Marathones. Of Laodicea in Phrygia, Archippus. Of Colossæ;, Philemon. Of Borea in Macedonia, Onesimus, once the servant of Philemon. Of the churches of Galatia, Crescens. Of the parishes of Asia, Aquila and Nicetas. Of the church of Æginæ, Crispus. These are the bishops who are entrusted by us with the parishes in the Lord; whose doctrine keep always in mind, and observe our words. And may the Lord be with you now, and to endless ages, as Himself said to us when He was about to be taken up to His own God and Father. For says He, 'Lo, I am with you all the days, until the end of the world. Amen.'" - Apostolic Constitutions, Book VII, XLVI
Evodius was ordained by Peter, and through Evodius the Patriarch of Antioch sits in St. Peter's chair.
-CryptoLutheran