MDG-= thanks for your considerate reply. see HaLeivi’s comments. According to the historical documents of the Persian empire (and greek), there were a slew of Persian kings between the churban and the Second Temple, a fact that would be difficult to square with “only” 70 years of galut bavel. I will try to find the copy of Tradition where this matter is discussed and quote from it.
I have not heard that we get thev 586 date from Josephus. I doubt that.
As far as your assertion of the dates coming from Torah and neviim-I think that -if you count the years of “malchus jehuda’ until the churban bayis rishon- you will find that it does not reach till 420 either.
The whole question depends upon the length of golus bavel- we are accustomed to say it is seventy years but this has no real source in the Tenach.