It seems to me that Josephus is entirely unreliable as a source of information regarding Jesus since we don't know where his simpathies lay but we can strongly suspect he had some kind of an agenda. On top of that it seems he has been tampered with. When, by whom, for what reason and which passages we can only guess at.

It seems that he wrote before the gospellers but what he actually wrote and for whom he wrote it is anybody's guess. Did you consider that the gospellers and He may have both plagiarised a third source?