Did Eastern Church Father St. John Chrysostom's Accept the Primacy of Peter?

Many non-Catholics like to argue that St. John Chrysostom, Doctor of the Church, did not accept the Primacy of Peter. I have written much about this in my book Upon This Rock. I have written on it extensively on my website HERE (scroll down to 3rd section “My Books”)
The Navarre Bible Commentary gets this correct in its comments on Acts 1:15 as it quotes our Catholic Saint and Doctor: “Peter is the ardent and impetuous apostle to whom Christ entrusted the care of his flock; and since he is first in dignity, he is the first to speak” (St John Chrysostom, Homily on Acts, 3).
Here we see Peter performing his ministry. Events will make for the gradual manifestation of the supreme role of government which Christ entrusted to him. His is a ministry of service—he is the servus servorum Dei, the servant of the servants of God—a min ministry given to none other, different from all other ministries in the Church. Peter will carry it out in solidarity with his brothers in the Apostolate and in close contact with the whole Church represented here in the one hundred and twenty brethren around him.
This account of Peter with the other apostles and disciples all brought together is described by St John Chrysostom in these words: “Observe the admirable prudence of St Peter. He begins by quoting the authority of a prophet and does not say, ‘My own word suffices,’ so far is he from any thought of pride. But he seeks nothing less than the election of a twelfth apostle and he presses for this. His entire behaviour shows the degree of his authority and that he understood the apostolic office of government not as a position of honour but as a commitment to watch over the spiritual health of those under him.
“The disciples were one hundred and twenty, and Peter asks for one of these. But he it is who proposes the election and exercises the principal authority because he has been entrusted with the care of all” (Hom. on Acts, 3).
Come on folks. St. John Chrysostom was a bishop of the Catholic Church, proudly, not a Baptist sectarian.