Okay, so looking into it further, it seems that the original claim for the six alleged schools and their opinions comes from "History of opinions on the scriptural doctrine of retribution" by Edward Beecher; his discussion of it begins on chapter 22. One may view it
here.
Having read through Beecher's arguments concerning the schools, while he does have some valid points to make, I also see serious problems with the argument. Essentially, its major basis amounts to "this theologian taught this and was really esteemed by these schools, so said schools agreed with them on it." Alexandria and Caesarea are stated to be universalists due to esteeming Origen. Antioch and Edessa are stated to be universalists due to having great affection for Theodore of Mopsuestia. Irenaeus is cited for Ephesus because he taught conditionalism, and Tertullian/Augustine for Carthage/Rome.
There are three problems I see with this. First, however revered a particular teacher was, this does not mean their "school" in general agreed with every point of doctrine. Not counting the writers of the Bible itself, Augustine was perhaps the single most influential theologian on the Catholic Church (the only other contender for that title is Aquinas), but not all of his ideas were fully accepted by it.
Beecher himself admits and points to several in those schools influenced by Theodore that rejected universalism. And I should note that John Chrysostom, who I will return to again later, was no believer in the doctrine and exerted considerable influence on Eastern churches. So this argument of "this highly esteemed teacher believed this, so the schools they were part of or influenced believed it" comes up wanting for me.
The second is that such individuals can only be counted as representative of their own time. What about before them? What about after them? Irenaeus (who we'll get to), for example, wrote in the last second century. What about Ephesus at other times?
Third is the question of whether these individuals had the beliefs that are ascribed to them. Theodore of Mospuestia I have often seen considered a universalist, even by those who are not universalist. But I am not sure if the evidence for this is actually that strong. It appears, at least in the arguments I have seen, to primarily rest on two points. The first is his writings, but the only writing I see cited that is
unambiguously universalist is a quote attributed to him in "The Book of the Bee" (
page 140) which was written 800 years later and thus a tenuous witness. Again, perhaps there is more, but I can only go by what I see people cite. The other is to claim there are universalist statements in the liturgies of his churches and their successors, but
this post on this very forum from someone familiar with the applicable churches says the claim is in error and comes from misunderstanding of the liturgy by outsiders.
Continuing on the question of whether the leaders believed what was ascribed to him, we turn to Irenaeus, presented as a believer in annihilationism/conditionalism. The chief prooftext for this is
Book 2, Chapter 34, specifically the statement "And, for this reason, the Lord declared to those who showed themselves ungrateful towards Him: “If you have not been faithful in that which is little, who will give you that which is great?” indicating that those who, in this brief temporal life, have shown themselves ungrateful to Him who bestowed it, shall justly not receive from Him length of days for ever and ever." This is cited as proof of Irenaeus's annihilationism.
However, that is assuming that is exactly what Irenaeus said. There is a problem with Irenaeus: Most of Against Heresies exists to us only in a Latin translation, and a poor one at that (
see here, which says the translation is of "the most barbarous character"). In cases like this, where whether it's an endorsing of something or not depends on the turn of a few words, I am hesitant to take much from it for fear it's the result of the translation being muddled. For the record, I for the same reason am very hesitant of trusting the quotes given in this topic from Irenaeus apparently affirming eternal damnation from Against Heresies, as those too fall under the question of how well it was translated.
This also brings up the question of, even if they did believe in such things, how influential those ideas of them were. Irenaeus, even if an annihilationist, hardly seems to have discussed it much. A highly influential theologian is far more influential in the areas they wrote much about, not things they made offhand references to a few times.
Still, that is concerning annihilationism, not universalism. We then come to Origen, and while his universalism seems quite clear (even if it is debated how far he went in those beliefs), we again come to the earlier problems in ascribing his views on one particular doctrine to the schools he is claimed to have influenced.
To be fair, later on Beecher does start discussing other teachers in
Chapter 29. However, his arguments here mostly amount to "they didn't criticize universalism, so they must have believed in it." That seems weak. But further, this is assuming he is portraying them accurately. I see one case where he is not doing so.
In
Chapter 30, he begins with John Chrysostom. He says Chrysostom mentions universalism a few times without criticizing it, and therefore believed in it. For example, he cites Chrysostom's commentary on 1 Corinthians 15:38 (I assume he means 15:28, as a different posting of the work has) and says that Chrysostom "simply says that the doctrine of universal restoration has been inferred from that passage, makes a striking statement of the result, and says nothing to refute the opinion." But having examined Chrysostom's exposition of it
here (Homily #39), I do not see what it is talking about. Granted, Chrysostom writes a bunch about that verse in dry language so I could have missed it in all of the text, but I didn't see it.
But the bigger problem is that Beecher completely skips over a writing of Chrysostom that proves, no doubt, that he was
not a universalist. Please examine
Homily #9 of the same epistle. Chrysostom is as blunt as can be: "This is no small subject of enquiry which we propose, but rather about things which are of the first necessity and which all men enquire about; namely, whether hell fire have any end. For that it has no end Christ indeed declared when he said, “Their fire shall not be quenched, and their worm shall not die.”" His statements immediately after that one reinforce his rejection of universalism further. This therefore leaves me with a question: If Beecher is this astoundingly inaccurate regarding Chrysostom, who was as clear as could be considering his rejection of universalism, how accurate am I to trust him in representing others?
To be fair, Beecher does seem to indicate Chrysostom preached eternal punishment: "Elsewhere Neander says that in his [Chrysostom's] field of labor he felt that the doctrine of eternal punishment was necessary to alarm the worldly and deter them from sin, and so he preached it to the multitude (“Ch. History,” vol. ii., p. 676, Torrey’s translation)." Two problems. First, the citation is inaccurate. Page 676 of Volume 2 is found
right here, and it's the Torrey translation for the record. Nothing about Chrysostom is there. Maybe he got the page number wrong, but Chrysostom is mentioned more than 200 times in the book and I'm not going to search for it. In any event, when one sees a passage as clear as the above from Chrysostom, one needs more than this kind of speculation to argue he believed in universalism. By this logic, I must as well argue that any early Christians who believed in universalism didn't
actually believe in it, but preached it to make people feel better!
All that said, while I believe Beecher overstates his case regarding how much universalism was believed in (at least in regards to his "six schools" argument), his arguments that belief in universalism did not seem to be considered a
problem (and something reasonable people could disagree about) in the early church were much stronger. One explanation for this could be, however, that universalism was far down the ladder on things to have disputes about. Things like Marcionism and Arianism were much bigger fish to fry, and compared to them, universalism vs. annihilationism vs. damnation was an intellectual curiosity. Only once these much more critical doctrines were settled did something like universalism become something to be critically examined.
THEREFORE, the conclusion of this long, rambling post is that, if Beecher is the source for the argument regarding the different schools, I have to confess I believe he comes up short in his argument. It simply relies too much on claiming a particular influential person believed in the doctrine and that therefore it must have been thought of highly in the areas they influenced (assuming the instances of claimed influence are as grand as was claimed by Beecher), plus a bunch of speculation on his part. One can take his points and put forward an argument that in the early centuries universalism wasn't looked down upon, but as an argument of the predominance of universalism, I feel it--at least in the form of the six schools argument--comes up short.