The Truth Shall Make You Free (1943)
Chapter 18 'Seven Times' of the 1943 book The Truth Shall Make You Free made some changes to the chronology surrounding the 'Gentile times', attempting to maintain the 606 BC to 1914 AD dates whilst dealing with the year zero issue created by Russell and Barbour's miscalculation [1, pp. 237–239].
This makes it clear that the “seven times” began with Nebuchadnezzar's overturning of Jehovah's typical Theocracy at Jerusalem, in 606 B.C. As long as the typical administration of God at Jerusalem operated at all, even imperfectly, in his name, that long there was some measure of national sanity and a partial exhibition of right rule among nations on this earth.
In Nebuchadnezzar’s time the year began counting from the fall of the year, or about October 1, our time. Since he destroyed Jerusalem in the summer of 606 B.C., that year had its beginning in the fall of 607 B.C. and its ending in the fall of 606 B.C.
Inasmuch as the count of the Gentile “seven times” began its first year at the fall of 607 B.C., it is simple to calculate when they end. From the fall of 607 B.C. to the fall of B.C. 1 is exactly 606 years. From the fall of B.C. 1 to the fall of A.D. 1 is one year, do not forget. Hence from the fall of B.C. 1 to the fall of A.D. 1914 is 1,914 years. Add now 606 years and 1,914 years, and the sum total is 2,520 years, ending in the fall of A.D. 1914. By this method Jehovah, who is an accurate Timekeeper as to his purposes, symbolically foretold that the ”times of the Gentiles”, that is, the ”seven times”, would continue and extend to the fall of A.D. 1914.
But regarding the date of Cyrus's first year, they remain unchanged on the year 536 BC [1, p. 151]:
It is well established that two years after the overthrow of Babylon in 538 B.C. by Darius the Mede and his nephew, Cyrus the Persian, the first year of Cyrus' exclusive rule began, which year was 536 B.C.
Issues
Tishri Reckoning
The first statement that 'in Nebuchadnezzar’s time the year began' in Tishri is somewhat ambiguous because it doesn't specify who's reign they are referring to. In the case of Nebuchadnezzar himself and the Babylonian empire they certainly used Nisan and not Tishri reckoning, on the other hand in Judah the situation is much less clear as was already explored in the Judean Chronology section.
Regardless of whether the regnal year began in the 1st or 7th month, we know from the Bible (2 Kings 25:3-7) that the walls of Jerusalem were broken and king Zedekiah captured in the 4th month (Summer), which according to the Truth book was Summer 606 BC. Counting 2520 years from Jerusalem's destruction in Summer 606 BC would bring us to Summer 1915 AD, yet the Truth book instead insists on counting 2520 years from the start of that regnal year in Autumn 607 BC (which adds up to Autumn 1914 AD).
But using this calculation would appear to contradict the earlier paragraph where it was said that 'as long as the typical administration of God at Jerusalem operated at all, even imperfectly' the 'seven times' could not begin – by starting the count in Autumn 607 BC, they are neglecting to count the 10 additional months of Zedekiah's administration operating in Jerusalem.
Cyrus First Year
It is not 'well established' that 'Darius the Mede' overthrew Babylon in 538 BC, he is not mentioned in any historical source other than the Bible [2, p. 581]. Nor is it 'well established' that Darius ruled for around two years before being succeeded by Cyrus. The Truth book provided no evidence for any of these claims.
References
[1] The Truth Shall Make You Free. Watch Tower Bible; Tract Society, 1943, [Online]. Available: https://ia600902.us.archive.org/5/items/WatchtowerLibrary/books/1943_myf_E.pdf.
[2] Insight on the Scriptures - Volume 1: Aaron-Jehoshua, vol. 1. Watch Tower Bible and Tract Society, 2018, [Online]. Available: https://www.jw.org/en/library/books/Insight-on-the-Scriptures/.