Some years ago I assisted an elder in his research on this topic. We found that the Society itself acknowledges that the Babylonian kings' list would prove that the Jews' stay in Babylon after Jerusalem's destruction was only 50 years. That is plainly stated in the book Babylon the Great Has Fallen! God's Kingdom Rules! published in 1963. And as sd-7 notes, Jeremiah prophesied about several nations being forced to serve the king of Babylon and not the Jews only.
There is of course a mountain of evidence to show that Jerusalem was destroyed in 587/586 BC. But we all know why the WTS clings to 607 BC. However, there is another way of bursting that balloon. As I have done more than once, I have challenged Witnesses to find the number 2520 anywhere in Scripture. They can't of course. And if they point to the book of Revelation and its equating "a time, times, and half a time" to 1260 days and 42 months, you can always counter with the fact that John is specifically told the corresponding time measures whereas Daniel is not.
Further buttressing this argument is a fact that the Society has deliberately buried and ignored. Nebuchadnezzar wrote two accounts of his madness. One is recorded in Daniel 4. The other is a clay prism written in cuneiform. In that document, Nebuchadnezzar says he was insane for seven seasons and those seven seasons amounted to parts of four lunar years. It seems that the Babylonians reckoned only two seasons in a year. The hot torrid summers (which the royal household spent in the mountains of present-day Iran), and the cooler, wet winters. Seven of those seasons would amount to three-and-a-half lunar years. That is nowhere near the seven years the Society figures.
There is one more thing I will add. The WTS can not prove that a "prophetic" year was 360 days long. A lunar year is 354 days and change. A solar year is 365 days and change. That has been known from the most ancient of times. Nobody had a 360 day year, nobody. The WTS should know this. So its assertion that a prophetic year was 360 days long is completely false.
I will conclude with this last damning point. Daniel was inspired by holy spirit to interpret Nebuchadnezzar's dream. Under the influence of that spirit what did he say the tree represented? Daniel 4:20, 22 answers, "The tree that you beheld, that grew great and became strong and the height of which finally reached the heavens...it is you, O king, because you have grown great and become strong." The teaching the WTS advances that there is some kind of "double application" of this dream has no foundation in Scripture. It is purely man-made, and certainly not of divine origin.