What is Hopeful Universalism?

[JSRG]

Scripture and universal tradition are not against this. For the first 500 years of the Church, there were four theological schools which taught Universalism without so much as a single whimper against them or anyone calling them out for "heresy." They were closed by Emperor Justinian, who zealously hated the teaching and did not wish it to exist in the Roman Empire of the East.

You are fond of making this claim about the "four schools" for "500 years". However, in an older topic, in direct response to you claiming this (without you offering any evidence), Der Alte observed:

I have seen this claim "Universal Restoration. 500 years of teaching it in four theological schools..." multiple times in this and other forums. But what I have never seen is any credible, verifiable, historical evidence supporting the claim. I only know of one source which makes the claim but does not itself provide any supporting evidence i.e. Schaff, Herzog Encyclopedia of Religious Knowledge
Link: Philip Schaff: Schaff-Herzog Encyclopedia Vol. : 0120=96 - Christian Classics Ethereal Library
Here is all that the article says.
Schaff, Herzogg Encycopedia of Religious Knowledge, Universalism, Vol. 12 p. 96

"In the West this doctrine had fewer adherents and was never accepted by the Church at large. In the first five or six centuries of Christianity there were five or six known theological schools, of which four (Alexandria, Antioch, Caesarea, and Edessa or Nisibis) were Universalist, one (Ephesus) accepted conditional immortality; one (Carthage or Rome) taught endless punishment of the wicked. Other theological schools are mentioned as founded by Universalist but their actual doctrine on this subject is unknown."​

I would appreciate anyone who could search and find something
1. Credible, definitely not Andy Anonymous' blog.
2. Verifiable, actually exists and readily available to the average person, not only available at a major university library with student ID..
3. Historical, something written at or near the times in question by a participant or direct eye witness.

And then he added:

"In the West this doctrine had fewer adherents and was never accepted by the Church at large. In the first five or six centuries of Christianity there were five or six known theological schools, of which four (Alexandria, Antioch, Caesarea, and Edessa or Nisibis) were Universalist, one (Ephesus) accepted conditional immortality; one (Carthage or Rome) taught endless punishment of the wicked. Other theological schools are mentioned as founded by Universalist but their actual doctrine on this subject is unknown."​

I'm going to critique my own source. Other than posts quoting this statement, I know of no other published credible source for the above information.
Note this statement "In the first five or six centuries of Christianity." The author of this doesn't even know exactly the time period when the early church supposedly believed in universalism.
Next this statement "there were five or six known theological schools" is self contradictory. Either the "theological schools" were "known" or they weren't. If they were "known" the author would have "known" exactly how many schools there actually were instead of saying "five or six known... schools."
Then the author mentions "other theological schools" but does not know what they taught.

You offered no response to that point in that topic. Now, few people have the time or interest to respond to every response to them, so I'm not going to begrudge you for that (I've certainly bowed out of plenty of arguments online). But the problem is, you still continue to make this "four schools, 500 years" claim in other topics repeatedly, and in the multiple times I've seen you assert it as fact, I've never seen you offer any evidence for it; you just assert it without evidence, even after (as noted before) being challenged on the lack of evidence. Maybe you just missed the above reply, but in any event you've still never offered evidence for it... at least not in the cases I've seen you repeat this claim.

Can you offer better evidence for it than two sentences in an encyclopedia article (by a universalist so not without bias) from more than a century ago?