Same history, no convergence

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Christian history holds that the historical trajectory went:  Jews, Jewish Christians, Christian Jews, Christians.

Jewish history says there was never any convergence.  Jewish history is accurate.

The trajectory went something like this:  

The TaNaKh was translated into the LXX.  

Greco-Romans got hold of it.  

Instead of translating the sentence "yehoshua homoshiach," they transliterated it into a name with an epithet:  Iesous ho christos.

They wanted to follow the "philosophy" without the surgery.

Paul "converted" from normative Pharasee practice, which held that only Judeans could engage in Temple praxis, and taught Greco-Romans how their praxis could be acceptable to Judean Temple community.  

The temple was destroyed.  

The Judeans kept going.  

The greco-romans weren't sure.  

The Kitos revolt occurred.  

The judeans kept going.  

The greco-romans weren't sure.  

Bar Cochba had a revolt.  

He restored the sovereignty of Israel.  

Hadrian conquered the restored state, destroyed bar Cochba and other Judean leaders and expelled Judeans.  

Judeans, attempting to incorporate the revolt into the Judean canon (as was done with the Maccabean revolt) wrote histories about it.  

Those histories seemed similar to the already-extant history of Apollonius of Tyana.  

Greco-Romans, on obtaining these Judean histories, assumed it meant that Judeans had finally come around to seeing the text their way, and that the texts were the "authoritative" Judean narratives of the hero they had created out of a transliteration.  

Judeans had not accepted the Greco-roman hero at all, and the texts were never meant to be read as “biographies” of the Greco-roman hero, but as a continuation of the narrative of the Judean people and their relationship with G-d, especially since that narrative included, however briefly, the restoration of the sovereignty of Israel. 

Judeans rejected the texts as having been wrongly interpreted and misleading about their intent, closed their community, rearranged how community texts would be presented to avoid any future similar misinterpretations (as had occurred with the LXX and the narratives post bar Cochba).

The distinction between "Judean" and "jewish" is necessary, because "jewishness" dates from after the bar Cochba revolt:  the early church claims the documents were "Judean" (meaning "jewish") in order to assert the authenticity of the identity of the hero-by-transliteration.  That authenticity does not exist.  The documents are, however, Judean in origin as they were intended to add the bar Cochba narrative to the Judean canon.