ithinkisee, you might try the following as an outline.
Read 2 Chron. 36:20. It clearly states that the Jews were servants to Nebuchadnezzar and his descendants until the royalty of Persia came to power. When was that? Obviously in 539 B.C. when Cyrus' armies conquered Babylon and killed Belshazzar. The Society has never commented on this passage, for rather obvious reasons.
Read Jer. 27:6,7. This clearly states, consistently with 2 Chron. 36:20, that the nations would serve kings in Nebuchadnezzar's line of descent by using the idiomatic phrase "serve him and his son and his grandson". Every Babylonian king after Nebuchadnezzar was either his actual son, his son-in-law, or, in Belshazzar's case, his grandson. The Society goes along with all of this.
Read Jer. 25:11, 12. It clearly states that the Jews and surrounding nations would serve Babylon for 70 years, and that when that 70 year period was fulfilled, or complete, the Babylonian king would be punished. Now, if Belshazzar's being killed, and the dynasty of kings of Nebuchadnezzar's line being ended, wasn't a punishment, I don't know what punishment is. This is also completely consistent, as Jeffro has pointed out, with Daniel 5, which clearly states that the Babylonian kingdom had been judged adversely and was punished the very night the handwriting appeared on the wall. Obviously, this punishment occurred in 539 B.C. The Society has commented only once about this, in a 1979(?) Watchtower article, but the explanation given is simply ridiculous -- that the punishment was actually Cyrus' letting the Jews go free in 537 B.C.
Hope this helps.
AlanF