Having discovered (from a Russian Old Believer source) a sketch of a flat earth with Slavonic lettering and features identical to those of Cosmas Indicopleustes, I'm interested to trace the history of how this tradition has apparently been preserved by some Old Believers as well as specifically how it passed from Byzantium to Russia in the first place.
Considering that in the ninth century Patriarch Photios wrote condescendingly of Cosmas Indicopleustes's book, I reckoned it would only help to distinguish where and among which schools of thought within Byzantium that Christian flat earth tradition persevered because flat earth was obviously no longer universal in Christendom after the followers of Muhammed revived many of the Greek writers.
The fact that Cosmas himself quotes many Nestorian writers and also that Nestorius's mentor Theodore of Mopsuestia was apparently a flat earth advocate suggests that Nestorianism picked up on the flat earth doctrine similar to the way that Seventh Day Adventists were particularly attracted to Rowbotham's movement in the nineteenth century.
Some writers (apparently beginning with Winstedt circa 1903) have erroneously assumed that Cosmas was a Nestorian because he quoted some of them on purely scientific matters, but they ignore that Cosmas explicitly calls the Virgin Mary the Mother of God which is something that Nestorians do not believe. He also resided at Saint Catherine's monastery in Sinai which is Orthodox (i.e. Chalcedonian) and not Nestorian.
Charles Johnson's friend Robert Schadewald thought that Syria in particular was a bastion of preservation of early Christian flat earth doctrine. It had a lot of Nestorians, and Orthodox Christians in Syria at the time apparently agreed with these scientific ideas even if not the theology of the Nestorians. John Chrysostom who wrote against the antipodes was from Antioch.
More to the point, a short and very explicit flat earth treatise attributed to Saint Dionysios the Areopagite (the Athenian disciple of Saint Paul from Acts chapter 17) survives only in the Syriac language.
Based upon what appears to be the historical trend of other ancient Christian traditions, my thesis is that Christian flat earth doctrine was universal prior to Muhammad. For example, Dionysios the Areopagite was Greek, Lactantius was from what is now Algeria. Saint Jerome was from Bethlehem in Palestine. Cosmas Indicopleustes was Egytian, et cetera.
After Muhammad, Christian flat earth tradition declined, and Syria became the bastion of its preservation. After the Crusades, flat earth Christian tradition also found sanctuary in Russia along with the rest of the Orthodox Christian tradition.