If you're looking for the Watchtower's argument for using the 607 BCE date, it appeared in the appendix of the book, Let Your Kingdom Come. Here it is:
Appendix to Chapter 14
Historians hold that Babylon fell to Cyrus? army in October 539 B.C.E. Nabonidus was then king, but his son Belshazzar was coruler of Babylon. Some scholars have worked out a list of the Neo-Babylonian kings and the length of their reigns, from the last year of Nabonidus back to Nebuchadnezzar?s father Nabopolassar.
According to that Neo-Babylonian chronology, Crown-prince Nebuchadnezzar defeated the Egyptians at the battle of Carchemish in 605 B.C.E. (Jeremiah 46:1, 2) After Nabopolassar died Nebuchadnezzar returned to Babylon to assume the throne. His first regnal year began the following spring (604 B.C.E.).
The Bible reports that the Babylonians under Nebuchadnezzar destroyed Jerusalem in his 18th regnal year (19th when accession year is included). (Jeremiah 52:5, 12, 13, 29) Thus if one accepted the above Neo-Babylonian chronology, the desolation of Jerusalem would have been in the year 587/6 B.C.E. But on what is this secular chronology based and how does it compare with the chronology of the Bible?
Some major lines of evidence for this secular chronology are:
Ptolemy?s Canon: Claudius Ptolemy was a Greek astronomer who lived in the second century C.E. His Canon, or list of kings, was connected with a work on astronomy that he produced. Most modern historians accept Ptolemy?s information about the Neo-Babylonian kings and the length of their reigns (though Ptolemy does omit the reign of Labashi-Marduk). Evidently Ptolemy based his historical information on sources dating from the Seleucid period, which began more than 250 years after Cyrus captured Babylon. It thus is not surprising that Ptolemy?s figures agree with those of Berossus, a Babylonian priest of the Seleucid period.
Nabonidus Harran Stele (NABON H 1, B): This contemporary stele, or pillar with an inscription, was discovered in 1956. It mentions the reigns of the Neo-Babylonian kings Nebuchadnezzar, Evil-Merodach, Neriglissar. The figures given for these three agree with those from Ptolemy?s Canon.
VAT 4956: This is a cuneiform tablet that provides astronomical information datable to 568 B.C.E. It says that the observations were from Nebuchadnezzar?s 37th year. This would correspond to the chronology that places his 18th regnal year in 587/6 B.C.E. However, this tablet is admittedly a copy made in the third century B.C.E. so it is possible that its historical information is simply that which was accepted in the Seleucid period.
Business tablets: Thousands of contemporary Neo-Babylonian cuneiform tablets have been found that record simple business transactions, stating the year of the Babylonian king when the transaction occurred. Tablets of this sort have been found for all the years of reign for the known Neo-Babylonian kings in the accepted chronology of the period.
From a secular viewpoint, such lines of evidence might seem to establish the Neo-Babylonian chronology with Nebuchadnezzar?s 18th year (and the destruction of Jerusalem) in 587/6 B.C.E. However, no historian can deny the possibility that the present picture of Babylonian history might be misleading or in error. It is known, for example, that ancient priests and kings sometimes altered records for their own purposes. Or, even if the discovered evidence is accurate, it might be misinterpreted by modern scholars or be incomplete so that yet undiscovered material could drastically alter the chronology of the period.
Evidently realizing such facts, Professor Edward F. Campbell, Jr., introduced a chart, which included Neo-Babylonian chronology, with the caution: "It goes without saying that these lists are provisional. The more one studies the intricacies of the chronological problems in the ancient Near East, the less he is inclined to think of any presentation as final. For this reason, the term circa [about] could be used even more liberally than it is."?The Bible and the Ancient Near East (1965 ed.), p. 281.
Christians who believe the Bible have time and again found that its words stand the test of much criticism and have been proved accurate and reliable. They recognize that as the inspired Word of God it can be used as a measuring rod in evaluating secular history and views. (2 Timothy 3:16, 17) For instance, though the Bible spoke of Belshazzar as ruler of Babylon, for centuries scholars were confused about him because no secular documents were available as to his existence, identity or position. Finally, however, archaeologists discovered secular records that confirmed the Bible. Yes, the Bible?s internal harmony and the care exercised by its writers, even in matters of chronology, recommends it so strongly to the Christian that he places its authority above that of the ever-changing opinions of secular historians.
But how does the Bible help us to determine when Jerusalem was destroyed, and how does this compare to secular chronology?
The prophet Jeremiah predicted that the Babylonians would destroy Jerusalem and make the city and land a desolation. (Jeremiah 25:8, 9) He added: "And all this land must become a devastated place, an object of astonishment, and these nations will have to serve the king of Babylon seventy years." (Jeremiah 25:11) The 70 years expired when Cyrus the Great, in his first year, released the Jews and they returned to their homeland. (2 Chronicles 36:17-23) We believe that the most direct reading of Jeremiah 25:11 and other texts is that the 70 years would date from when the Babylonians destroyed Jerusalem and left the land of Judah desolate.?Jeremiah 52:12-15, 24-27; 36:29-31.
Yet those who rely primarily on secular information for the chronology of that period realize that if Jerusalem were destroyed in 587/6 B.C.E. certainly it was not 70 years until Babylon was conquered and Cyrus let the Jews return to their homeland. In an attempt to harmonize matters, they claim that Jeremiah?s prophecy began to be fulfilled in 605 B.C.E. Later writers quote Berossus as saying that after the battle of Carchemish Nebuchadnezzar extended Babylonian influence into all Syria-Palestine and, when returning to Babylon (in his accession year, 605 B.C.E.), he took Jewish captives into exile. Thus they figure the 70 years as a period of servitude to Babylon beginning in 605 B.C.E. That would mean that the 70-year period would expire in 535 B.C.E.
But there are a number of major problems with this interpretation:
Though Berossus claims that Nebuchadnezzar took Jewish captives in his accession year, there are no cuneiform documents supporting this. More significantly, Jeremiah 52:28-30 carefully reports that Nebuchadnezzar took Jews captive in his seventh year, his 18th year and his 23rd year, not his accession year. Also, Jewish historian Josephus states that in the year of the battle of Carchemish Nebuchadnezzar conquered all of Syria-Palestine "excepting Judea," thus contradicting Berossus and conflicting with the claim that 70 years of Jewish servitude began in Nebuchadnezzar?s accession year.?Antiquities of the Jews X, vi, 1.
Furthermore, Josephus elsewhere describes the destruction of Jerusalem by the Babylonians and then says that "all Judea and Jerusalem, and the temple, continued to be a desert for seventy years." (Antiquities of the Jews X, ix, 7) He pointedly states that "our city was desolate during the interval of seventy years, until the days of Cyrus." (Against Apion I, 19) This agrees with 2 Chronicles 36:21 and Daniel 9:2 that the foretold 70 years were 70 years of full desolation for the land. Second-century (C.E.) writer Theophilus of Antioch also shows that the 70 years commenced with the destruction of the temple after Zedekiah had reigned 11 years.?See also 2 Kings 24:18?25:21.
But the Bible itself provides even more telling evidence against the claim that the 70 years began in 605 B.C.E. and that Jerusalem was destroyed in 587/6 B.C.E. As mentioned, if we were to count from 605 B.C.E., the 70 years would reach down to 535 B.C.E. However, the inspired Bible writer Ezra reported that the 70 years ran until "the first year of Cyrus the king of Persia," who issued a decree allowing the Jews to return to their homeland. (Ezra 1:1-4; 2 Chronicles 36:21-23) Historians accept that Cyrus conquered Babylon in October 539 B.C.E. and that Cyrus? first regnal year began in the spring of 538 B.C.E. If Cyrus? decree came late in his first regnal year, the Jews could easily be back in their homeland by the seventh month (Tishri) as Ezra 3:1 says; this would be October 537 B.C.E.
However, there is no reasonable way of stretching Cyrus? first year from 538 down to 535 B.C.E. Some who have tried to explain away the problem have in a strained manner claimed that in speaking of "the first year of Cyrus" Ezra and Daniel were using some peculiar Jewish viewpoint that differed from the official count of Cyrus? reign. But that cannot be sustained, for both a non-Jewish governor and a document from the Persian archives agree that the decree occurred in Cyrus? first year, even as the Bible writers carefully and specifically reported.?Ezra 5:6, 13; 6:1-3; Daniel 1:21; 9:1-3.
Jehovah?s "good word" is bound up with the foretold 70-year period, for God said:
"This is what Jehovah has said, ?In accord with the fulfilling of seventy years at Babylon I shall turn my attention to you people, and I will establish toward you my good word in bringing you back to this place.?" (Jeremiah 29:10)
Daniel relied on that word, trusting that the 70 years were not a ?round number? but an exact figure that could be counted on. (Daniel 9:1, 2) And that proved to be so.
Similarly, we are willing to be guided primarily by God?s Word rather than by a chronology that is based principally on secular evidence or that disagrees with the Scriptures. It seems evident that the easiest and most direct understanding of the various Biblical statements is that the 70 years began with the complete desolation of Judah after Jerusalem was destroyed. (Jeremiah 25:8-11; 2 Chronicles 36:20-23; Daniel 9:2) Hence, counting back 70 years from when the Jews returned to their homeland in 537 B.C.E., we arrive at 607 B.C.E. for the date when Nebuchadnezzar, in his 18th regnal year, destroyed Jerusalem, removed Zedekiah from the throne and brought to an end the Judean line of kings on a throne in earthly Jerusalem.?Ezekiel 21:19-27.