Hmmmmm!!!!!!!!
You have the starting point square at 539B.C.
J.B. Pritchard, Ancient Near Eastern texts rel, 3rd ed. (Princeton University Press, 1969)
A.K. Grayson, Babylonian and Assyrian chronicle (Locust Valley, J.J. Augustin, 1975)
September/October 539 BC the Persian and Babylonian armies met at Opis, east of the Tigris. Cyrus was victorious, the cities of Sippar and Babylon surrendered, Nabonidus was captured, and the Persian king entered Babylon as the new ruler.
Even though you don’t show secular reasoning to establish timeline, there seems to be acceptance of secular time frame. So if you’re willing to accept the Babylonian army simply gave up in 539BC. Then, this would be a point of debate.
Now the lunar/solar cycle to my reckoning started later around 5 BC. Before, it was lunar. There’s also some confusion that certain Kings would suggest the start of the calendar year.
So without having access to the above books, I would be able to calculate with more certainty that will suggest the Babylonians surrendered in 538BC, thus bring into line the decree given by Cyrus the Great in that year in the month of Nissannu (Babylonian)-Nissan (Jewish)-March/April (Julian) which was the harvest of onions season. Since it was harvest time, then Cyrus most likely made his decree in the planting season which allowed the Jewish people time to prepare and go back to Jerusalem by the last harvest in Addaru (Babylonian)-Adar (Jewish)-February/March (Julian).
When people make argument of calendar years, they automatically have a mindset of confusing year tables. While the Julian calendar runs from January-December 12 months, The Babylonian and Jewish calendar runs from March-February 12 months.