Peter, here are my thoughts on the answer to your question. To me, it all boils down to who you're going to trust: experts or the clergy.
There are scholars who have spent their entire adult lives studying neo-Babylonian history and archaeology. These scholars have examined the primary sources and unanimously agree that Jerusalem fell in either 586 or 587. For evidence of this, look in any (I mean any) encyclopedia. Every single one will say that Jerusalem fell in 586 or 587.
These same scholars use the same evidence to support their conclusion that Babylon fell in 539 BC. Interestingly, the Watchtower Society agrees with this. But they disagree with the 586/587 date--which is supported by the same scholars looking at the same evidence! That should tell you something.
Think about the motives of the parties involved. Neo-Babylonian scholars have no incentive to fabricate the 586/587 date. In fact, if a scholar were able to prove that that another date was correct, that would increase his prestige! But on the other hand, the Society has tremendous incentive to argue for the 607 date. Without it, the entire system of Watchtower chronology is wrong.
So, on the one hand, we have the experts in the field, with no motive to lie about 586/587. On the other hand, we have the clergy (the WTS) who must argue for 607 in order to survive and thus have every motive to discredit 586/587 at all costs. Who are you going to believe?