“If so, what are we left with aside from modern archeological evidence?” You mean apart the fact that Christianity still exist? Well, we depend on texts written after the Christ’s death, and most of the texts we study were written and biased. But we have other authors speaking of Christianity. I can’t remember the names, but one spoke about the “mud of the Euphrates”, and another one complaining about “again a Jew Sect”.
We also know that the conversion didn’t work so well at the beginning, because we have some records in Greece, showing a decline of the few converts in this country. Christianity was in concurrence with the cult of Isis and Mithra.

We also know that Jesus as preacher was part of an intellectual Jewish movement (the Esseinians, first builders of kind of religious community in Qumran) which was unhappy of the Priest of the Temple and their interpretation of the Dogma. They were practising chastity, had the benediction of the bread and the wine, baptised, and didn’t eat any animals except fish, exactly what did the early Christians and then the Catharses.

“I believe it's widely accepted by historians” Not really. This passage is highly suspect, on contrary. It doesn’t match with the rest of the text, in content and style.
Flavius Joseph himself is questionable about his biography. What he pretended to be and studied is hardly believable. Well in fact it can’t be true. More, living under the reign of Nero, it is difficult to imagine he will write such thing about the Christians.

Flavius Josephus wrote first work, the Jewish War, in Aramaic, and presented it to Vespasian between 75 and 79. An assistant translated it into the language of scholars of his days, Greek. So, you can see there is a lot a possibilities to transform and modified the texts, and even more after, during the development of Christianity, when the only people doing that were the one who had a big interest to show that Christ was a reality.