"We do have a lot of Scripture detailing what traits and gifts a leader should possess, but the monobishphoric structure did not develop until the second century."
That's simply incorrect, WF. We have historical evidence of both +Ignatius and +Polycarp having been bishops, and called that, in the 1st century during the life of at least +John.
Is this the time where I tell everyone what my mother said when she read Timothy? Unconsciously paraphrasing Tertullian she said,"All those bishops -- and only one poor wife? Poor THING!" My Mom was maybe not a very holy woman but she was as funny as could be.
Your right you do have historical records that some churches had bishops. However, your argument falls in that they do not say they were appointed by the Apostles. Also, you find most churches were run by leaders appointed by the congregation. For example, Clement was upset with Corinth because they had removed leaders he liked and installed others they felt were more appropriate.
John does not refer to himself as a Bishop, but as an elder towards the end of his life.
The only way you can make a claim to a special nature to the succession of your church leadership would be in the ordination process, or laying on of hands. Your claim falls if it's based on Apostles appointing leaders because they did not do that.