Tricky, but obvious. IIRC, the word ‘catholic’ is not capitalized in the way Ignatius used it, as the ‘universal’ church, the ekklesia in total, because he was referencing the several Bishoprics. Ignatius was associated to the Bishopric of Antioch. The first acknowledge use of the word is the 14th century, for the way you are trying to push it.
But the Catholic Church of today is a direct continuation of the church described by Ignatius. To claim otherwise is to go against history. By the way, there are over 5000 Catholic bishops around the world. The Catholic Church is more than just the Bishop of Rome, no matter how much some Protestants would like to portray it so.
The first acknowledge use of the word is the 14th century, for the way you are trying to push it.
Try again:
For in the Catholic Church, not to speak of the purest wisdom, to the knowledge of which a few spiritual men attain in this life, so as to know it, in the scantiest measure, indeed, because they are but men, still without any uncertainty (since the rest of the multitude derive their entire security not from acuteness of intellect, but from simplicity of faith,)—not to speak of this wisdom, which you do not believe to be in the Catholic Church, there are many other things which most justly keep me in her bosom. The consent of peoples and nations keeps me in the Church; so does her authority, inaugurated by miracles, nourished by hope, enlarged by love, established by age. The succession of priests keeps me, beginning from the very seat of the Apostle Peter, to whom the Lord, after His resurrection, gave it in charge to feed His sheep, down to the present episcopate. And so, lastly, does the name itself of Catholic, which, not without reason, amid so many heresies, the Church has thus retained; so that, though all heretics wish to be called Catholics, yet when a stranger asks where the Catholic Church meets, no heretic will venture to point to his own chapel or house. Such then in number and importance are the precious ties belonging to the Christian name which keep a believer in the Catholic Church, as it is right they should, though from the slowness of our understanding, or the small attainment of our life, the truth may not yet fully disclose itself. But with you, where there is none of these things to attract or keep me, the promise of truth is the only thing that comes into play. Now if the truth is so clearly proved as to leave no possibility of doubt, it must be set before all the things that keep me in the Catholic Church; but if there is only a promise without any fulfillment, no one shall move me from the faith which binds my mind with ties so many and so strong to the Christian religion. (St. Augustine, Against the Epistle of Manichaeus called Fundamental, 4:5, A.D. 397)The Catholic Church is here opposed to heretical churches. He also points out apostolic succession and Petrine leadership.