I do not accept your tabulation or your methodology The first year of Cyrus is given by Jack Finegan in his Handbook of Biblical Chronology, 1998, p.180, Table 88 as 538/537 BCE. Therefore, that first year was evenly divided or lay equally between the 538 and 537, this means that the seventh month would fall not on the side of 538 but as the beginning of 537 BCE.
Celebrated WT scholars have said in former times that "Whether the time of their arrival and resettlement there be reckoned as in the first or second full year of Cyrus' reign makes no difference. In either case, as above shown, Cyrus' decree and the Jew's resettlement could both be in 537 BCE".
If the Society's presentation of matters is impossible as you argur then how is that this is the first time that such claims have been raised? Carl Jonsson who is very familiar with calendation would seized upon such a blatant error if in fatc such an error is made. Even in Jonsson's recent fourth edition of his GTR he is not critical of the Society's explanation of 537 BCE as the year of the Return. Jonsson in the footnote 2 on page 90 states "The context seems to imply that this was still in the "first year of Cyrus". Most authorities, therefore, conclude that this was in the autumn of 538 BCE and not in 537 BCE as the Society insists". However, Jonsson cites two authorities in support of this view but a close reading of that material does not clarify the matter greatly.
If you have conclusive proof that you are right and that 537 BCE is utterly and postively wrong then write to the Society and put your view forward or further prepare and submit an article to some scholarly journal in order that all scholars can know for certainty the precise year for the Return.