So your only source for the years was Wikipedia? Did you track down the Jewish sources for Wikipedia's information?
I'm sure you saw this comment in the article:
The chronology given above, based on Josephus, however is not undisputed, with some alternatively placing Jaddua during the time of Darius II and some supposing one more Johanan and one more Jaddua in the following time, the latter Jaddua being contemporary of Alexander the Great.
I know the Josephus reference you gave. I was puzzled by Wikipedia's comment that the chronology of priests was based on him and yet I could find no years. So again, where do the years come from?
Bible scholars are aware of the passage in Josephus too, yet many still believe the Darius in Neh. 12:22 is Darius II. I also know you are aware how some of the historical details found in Josephus' work are either plain wrong or conflict with other sources, e.g. compare Ant. XI, 2.22f. with Ezra 4:11f.
I'm not convinced you have all your ducks in a row yet. I'm going to scour Josephus more thoroughly, however.
There are plenty of scholars who do not believe the Bible is God-inspired but still study it as historical and cultural literature. There are those who do believe the Bible is God-inspired and yet opt for Darius III. So again, a conclusion about which Darius it was has to have been based on better grounds than just wanting to squeeze the book of Nehemiah into a narrower time-frame to fit a religious ideology.