You need to reread Josephus again because he said nothing about the seventy years indicating Babylonian supremacy in fact quite the opposite for this period referred to exile, servitude and desolation from the Fall to the Return.
Your postulation simply doesn't fit with all of the facts as a whole. As usual, you simply ignore the points that completely invalidate your flawed interpretation and observe only a subset of the facts without regard for the entire context.
The reigns for the Neo-Babylonian period vary from secular history as compared with the cunieform records and Josephus also gives different figures for some of these fellows. Whatever the case we have the troubling seven years for Nebuchadnezzer and the twenty year gap problem. Hence, a 'dog's breakfast'.
The 'dog's breakfast' as you like to call it is purely a creation of the Society. The 'twenty year gap' is a creation solely of the Society's flawed interpretation. You have been told many, many times that the supposedly 'missing' seven years of Nebuchadnezzar is simply a red herring, as no other king took his place, and for business purposes, it still would have been considered Nebuchadnezzar's rule during any period for which he was away but still officially king. Extant Babylonian and Egyptian chronology synchronize perfectly to verify that there is no 20-year gap in reality. Even if both chronologies were completely wrong, the chances of them both having the same error at the exact same place is infintesimally small. Added to that, Josephus confirms my reckoning of 182.5 years from the end of the ten-tribe kingdom until the first year of Cyrus. The more information is brought to light, the more accurate my interpretation seems to be. On the other hand, you are forced to claim that the 182.5 years must just be "irrelevant" because it is incompatible with your interpretation.