In researching the times of the first congregation it is hard not to run into the historian Josephus. Flavius Josephus... Who was he?
1. A Messianic Jew?
2. A Jewish traitor turned historian?
3. Only out for himself?
Yosephus claimed to be a Kohen (Priest) of the family and course of Yhoyarib, (the first course in the rotation of the priestly courses), which was also the claim of the Hasmoneans or Maccabees, which Yosephus also claimed of himself, that is, Hasmonean descent.
Some modern Jews do count Yosephus as a traitor. Others in the field of scholarship also have claimed that an early church scribe or scribes, (who would have had access to Roman government archives), inserted the pro-Christianity pro-Christ statements into the writings of Yosephus, (the name Eusebius immediately comes to mind).
One of the very interesting things about the writings of Yosephus is what he says in several places about there having been three mains sects of the Yhudim, even saying that all three had been around for a long time, with the fourth sect, that of the Rebels, being the only sect which was less than a century old, (having arisen at the time of the census of Quirinius). And yet Yosephus, supposedly being a Perushi, (Pharisee), gives way more information about the so-called Essenes than any other sect. Perhaps he felt that everyone already knew all about the Pharisees and Sadducees and decided to spend so much more time and space on the Essenes? I dunno. Perhaps maybe he was rather a closet Essene? I dunno, but he sure has some kind words for the Essenes.
Regarding your "church ages" hypothesis, if you go back beyond the first century, I suspect that the Essenes would end up being the intertestimental missing link. In fact, it is possible that you might be reading a document written by one of them whenever you open up the epistle to the Hebrews.