The JW's believe the greater fulfillment of the Dream of the Tree began in 607 BC when Jehovah allowed the "tree" of Davidic kingship to be cut down. 607 BC was well before Nebuchadnezzar had even had the dream and well before Belteshazzar had interpreted it. Therefore in the JW interpretation, the prophetic fulfillment actually starts before the prophecy is given.
OK, this post is getting old, but I'm going to throw my 2 cents in anyway...
As for the dream happening before the fall of Babylon, how do we know that? It's probably very simple. I just don't have a Bible with me at the moment. We know there was more than one deportation to Babylon. Could Daniel have been carried away in one of the earlier ones before the final destruction? And if he was, could this prophecy have been fulfilled before the destruction of Jerusalem. You might say there was no 7 year time period that Nebuchadnezzar was missing-in-action before the destruction of Jerusalem, but then again nobody said it was 7 years. Could have been 7 days or 7 months.
To me, the more important weak link with this "greater fulfillment" thing is that Nebuchadnezzar was king of Babylon. The same Babylon that came to represent all kinds of false worship. His being stripped of his kingship for 7 times is supposed to foreshadow God's rule being stripped from the earth for 7 prophetic times. The JWs call Jesus the "greater Abraham". Do they call God or God's rule the "greater Nebuchadnezzar"? I don't think so. Why? Because in JW terms, Nebuchadnezzar represents the other side of the coin, the opposite of the Jews. You're going to tell me this guy foreshadows God's kingdom?
And as for 7 years, I know the current Jewish calendar has 12 30-day months and every 5 or 6 years, they throw in a 13th 30-day month to balance things out for the missing 5.25 days. So, if Nebuchadnezzar was missing-in-action for 7 years, by the Jewish calendar, those years had to include 1, if not 2 390 day years. So now, instead of 7 * 360 = 2520, we have an extra 30 or 60 days. So, even **IF** 607 were right, the extra 30 or 60 days would land you in 1944 or 1974.
Further weak points. You're going to tell me that Nebuchadnezzar went crazy for 7 years, then all of a sudden he's better and the person that took over in his absense is going to let him come right back in and rule the nation? 7 years of being crazy is a LONG time. That's like pulling Charles Manson out of prison and giving him a presidential cabinet position. What interim leader is going to step aside? On the other hand, what if the 7 times were months? That might give people more confidence that he's going to be OK. What if he was only gone 7 days? The shorter the time period, the more people are going to trust him to lead again.
OK, you say God placed him back. It doesn't matter whether his interim leader wanted to step aside or not. God grants power to who he wishes and takes it away from who he wishes. OK, but I thought the whole world was ruled by Satan. JW logic says how could Satan offer all the kingdoms of the world to Jesus unless he controls them? How can he control the nations if God is the one who grants power and takes it away?