Again, I'm not expert (My main historical interests are political and economical, although I do do a lot of reading on Renaissance humanism), but wouldn't heresies like Arianism count? Meletius, too, led a small schism from the Creed.
Especially under the wing of an astute pagan Emperor, smaller sects of Christianity could easily survive and grow.
The thing that your missing is that there were a series of Arian Emperors, and many high-ranking church officials followed the heresy. It was during one of these Arian Emperors' reigns that the Goths were converted to Christianity of the Arian heretic persuasion. However, despite this high-level support, the Arians with their anti-Nicaean heresy were never able to gain control and make their heretical ideas official church theology.
These were CHRISTIAN Emperors, practicing one of the most popular heresies that Nicean Orthodoxy ever faced, who put their own supporters of the same heretical persuasion into positions of power within in the Church. And they were unable to turn back Nicaea.
So what was an Apostate Emperor, who was opposed to the very idea of Christianity, and committed to the creation of what would have essentially amounted to a Neo-Platonic/Pagan Catholic Church, going to do?
Even with just one Orthodox church, though, there were several other universalist religions out there competing with Christianity.
Christianity was head and shoulders more organized than the other religions. Nicaea was demonstrative of the organization of the Christian Church. Hundreds of bishops, dividing the Empire into neat little territories, in charge of specific populations, all preaching the same message, "There is one holy catholic apostlic church . . ." it was powerful stuff as OTL demonstrated.
So have fun breaking that up, cause no one was able to OTL.
I'm not sure I agree; what were Arians doing in Ostrogoth Italy and North Africa, then?
Okay, these were the religions of barbarian tribes, but they had their own institutions.
The Germanic tribes who converted to Arian Christianity maintained a parallel clergy, but they maintained it because their Arian heresy kept them apart from the Roman population. The Germans wanted to maintain themselves as the political and military elite, and the best way to keep from mixing was to run parallel legal and religious systems, which they did. At the point that the Germans were maintaining their own Arian clergy however, the larger battle between Arians and Nicaeans over who would control the Christian Church had been won by the Nicaeans.