Well I don't think the verse is saying that Nebuchadnezzar will live in the last days, doesn't it say that God will show him what will happen in the latter days? In other words God gave Nebuchadnezzar this dream to reveal to him what will happen in the future. Like pharaoh had the same sort of dream, and it was pointed out that there will come seven years of plenty and seven years of famine, so the dream that pharoh was given was given to show the future events, it could be possible to read these verses in Daniel this way.
So if in fact Nebuchadnezzar is infact representing this head of Gold, is it also true that belshassar was also representing this head of Gold, since Babylon was represented as Gold. If then Nebuchadnezzar was the head, who then are the chest and arms and the brass and the iron?
Numbers 24:14-17 the use of the phrase "latter days" is refrencing the time when Jesus comes to the earth, and make the ultimate sacrifice. If the "latter days" is in refrence to the last days then Jesus has yet to make this sacrifice for us, and we should still be keeping the law, doing the ceremonial services, and a whole plethora of other complications arise, so in my thinking, although "latter days" can mean last days, if we apply it to the dream, then again we have complications as you have just stated, that if it is so why is it that Nebuchadnezzar is not alive now. So I think latter days, could mean something other than the last days in this context.