We have a set of Babylonian records (the Babylonian Chronicles) which give dates of major events in their history for this period, including astronomical occurrences. From this, we find that the first fall of Jerusalem (Jehoiachin deposed, Zedekiah installed as king) was on 16 March, 597BC. We don't have a direct Babylonian record for the second fall, but going with Jeremiah 52:6 tells us that Jerusalem fell in the summer of the 11th year of Zedekiah's reign, i.e., 587BC. This is consistent with the Babylonian chronology. Note that there was some debate as to how regnal years should be counted - different nations at the time used different system - so some (initially Thiele in the 1950s) have argued that the 11th year meant 586 instead, and you'll see this date in various sources. However, I think this has now been settled to everyone's satisfaction - or at least those who care about such things! I wasn't aware that anyone had put forward any alternative date, so would be interested in knowing where your 607 came from.

Finegan, Handbook of Biblical Chronology, discusses this issue at great length, particularly the issue of regnal years, and cites the relevant archaeological papers (mostly dating back to the 1950s).