John,
Here is what I found with a simple Google search for:
six schools of early church
1. (The first hit) https://en.wikipedia.org/wiki/Christian_universalism
"Christian universalism"
Under the sub-heading "Eternal Hell in Christian history"
"According to Theologian Edward Beecher in the first four centuries there were six main theological schools and only one of them advocated the idea of eternal Hell.[17]"
and [17]:
Edward Beecher, "HISTORY OF OPINIONS ON THE SCRIPTURAL DOCTRINE OF RETRIBUTION"[4] "What, then, was the state of facts as to the leading theological schools of the Christian world, in the age of Origen, and some centuries after? It was, in brief, this: There were at least six theological schools in the Church at large. Of these six schools, one, and only one, was decidedly and earnestly in favor of the doctrine of future eternal punishment. One was in favor of the annihilation of the wicked. Two were in favor of the doctrine of universal restoration on the principles of Origen, and two in favor of universal restoration on the principles of Theodore of Mopsuestia."
2. (Second hit) https://en.wikipedia.org/wiki/Universal_reconciliation
Universal reconciliation
Early Christianity
In the first 600 years of Christian history, researchers have identified six main theological schools concerning apokatastasis. Four of them were Universalists, one taught "conditional immortality" and the last taught Eternal hell.[14] Many early church fathers have been quoted as either embracing or hoping for the ultimate reconciliation of God with His creation. Those that did not embrace the teaching, such as Augustine, acknowledged that it was a common enough belief among Christians of the day.[15][16] The concept of a final restoration of all souls particularly had large appeal in the East during the fourth and fifth centuries.[2]
N. (Farther down) https://www.patheos.com/blogs/richardmurray/2019/07/four-reasons-the-early-church-did-not-believe-hell-lasts-forever/
Four Reasons the Early Church Did Not Believe “Hell” Lasts Forever
Also looks good, (Only read some parts.)
Also in the past, I have read that a number of the early church leaders knew that universal reconciliation was true, but did not teach it because they believed people would stop living righteously, and go back into the world. So actually they were held to 'the faith' by fear, not by a loving relationship with the Lord Jesus. And indeed many still are! But I believe He will say to them "I never knew you." How sad that many think that living a 'Christian' life because of fear will 'save' them.
A couple of years ago or so, I was in contact with several brothers all at the same time who held the 'annihilation' view. I had long conversations with some of them, and really had to wrestle with the scriptures they presented. After months of conversations and seeking the Lord for light, I came to an understanding much fuller than what I previously had. It brings all those scriptures and more into perfect harmony. It is a bit of a big subject, and I may consider writing more about it. Forgive me for just a little 'teaser' here, but I did a study of 'twin(s)' in the Bible, and learned some most fascinating connections. Lets keep talking!
Blessings,
Harvey
(2020/03/10 for John C.)