Either you form your theology and choose the teachings that support your theology, you choose the teachings and form a theology from that ... or you look at those men as fallible human beings that sometimes got it right and sometimes got it wrong and use the Bible as your source of doctrine and practice.
You are correct. Some of them did not agree with others. Those differences got ironed out in Councils of the Catholic Church when they met to discuss those difference. Usually heresies were involved if my memory serves me correctly.
Actually, they did.
If you compare their writings to the writings of the Gnostics, the Arians, the Manichaeans, the Pelagians, the Montanists, etc. it becomes clear that their points of difference among themselves were quite small compared to their agreement on important issues: most signally their unanimity on the Nicene Creed.
Most of the "incoherencies" that are perceived in them today stem mostly from disputes between Lutherans, Calvinists and Catholics on certain idiosyncratic features of one father's, Augustine's, writings.
All the Fathers are anachronistically viewed through the lens of the Reformers' interpretation of Augustinian theology.
But the Fathers all agreed on what we today call "mere Christianity" after C.S. Lewis' phrase: orthodox Christianity is their consensus.