I believe that the Zadokites' beliefs constituted a part of this eventual Christian edifice, along with all the other too many to count Gnostic sects and brotherhoods at the time, such as the Essenes.
Within a handful of years of Jesus' supposed death, we find Christian communities all over the eastern Medterranean, their founders unknown ... Paul could not possibly account for all the Christian centres across the empire; many were in existence before he go there ... A form of Christian faith later declared heretical, Gnosticism, clearly preceded the establishment of orthodox beliefs and churches in whole areas like northern Syria and Egypt.
Indeed, the sheer variety of Christian expression and competitiveness in the first century, as revealed in documents both inside and outside the New Testament, is inexplicable if it all proceeded from a single missionary movement beginning from a single source ...
Paul meets rivals at every turn who are interfering with his work, whose views he is trying to combat. The "false apostles" he rails against in 2 Corinthians 10 and 11 are "proclaiming another Jesus" and they are certainly not from Peter's group. Where do they all come and where do they get their ideas? The answer seems inevitable: Christianity was born in a thousand places, in the broad fertile soil of Hellenistic Judaism. It sprang up in many independent communities and sects, expressing itself in a great variety of doctrines.
Earl Doherty, The Jesus Puzzle.
The Essenes seem to have had their teachings lifted in an out-and-out cut and paste job by the canonisers like Irananeus and put into the New Testament, as shown by my earlier table. There were also other branches of the Essenes referred to by Philo called the Eclectics and the Ascetics.
Philo also tells ua about the Thereputae, who had parishes, churches, bishops, priests and deacons long before the Christian era. The Theraputae were based in Alexandria, dubbed by some as the Crucible of Christianity, and so maybe we should look at these guys next.