With regard to the two Torahs, I'm aware of the Oral Torah, which Christian commentators often label the oral tradition or oral law. Most often they note it as a major point of difference between the Pharisees and Sadducees. I don't think I knew (though with age, memory is less certain than in the past)that the earliest versions of the Mishnah "espoused teachings without reference to earlier sources."
If I understand you correctly, you think a key difference between Jesus and the Pharisees was that "the rabbis operated within a large community of scholar-saints who challenged one another's teachings in order to separate truth from mere opinion, while Jesus appears to make his teachings without benefit of colleagues." Jesus, at the very least, may have seen himself as part of a prophetic tradition, the lone voice challenging the consensus of the community. From later Christian perspective, of course, he spoke a corrective word from God. On a personal note, given your qualms about the limits of community, I wonder how you feel about the contrast you've noted.
Let's turn back to "neighbor" and the first century division between Judaism and Christianity. The division was well under way before the destruction of Jerusalem in the first century and an established fact well before the start of the second century. In the end the core issue boiled down to something along the following lines. Could a gentile become a full-fledged member of the community without becoming first a Jew (circumcision, food laws, etc).
Paul took the position that gentiles could do so. Others within the broader community disagreed. Peter seems ultimately to have agreed with Paul in theory and occasional practice, even as he found it difficult to handle the resultant pressure. James, along with the leadership in the Jerusalem church, ultimately chose to pursue a moderate course, which is essence exempted gentiles from most Jewish practices, though keeping in place certain food restrictions connected with idolatry. In short, the three apostles had to contend with a culture war.
Nineteenth and early twentieth century scholarship posited sharp and clear divisions between two camps within Christianity. As it turns out, the situation was considerably more complicated. Tensions, though, were quite real. Toward the end of his life, Paul recognized the reality of the division. By the time Revelation was written (almost certainly in last decade of the first century), the division appears to have been deep and virtually complete.
All that is to say that I suspect the war of liberation against the Roman occupation may have put nails in the coffin but little more.
"One table" or "God's Table" is the metaphor and reality with which we must come to grips. You state the matter well. The truth of the matter, I think, is that all of us already sit at that table. At the risk of understating the matter, I think table manners are the challenge. Somehow we must learn to believe and act as if it's a common table, rather than one we can or dare to claim exclusively for ourselves (and others we may like).