I don't know how the Levitical priesthood's role will change in Eternity--the Bible doesn't give us enough information on that Age to do more than speculate wildly. By the same token, we don't know how King Yeshua's role will change--He won't need to rule the nations "with a rod of iron" when all evil is done away with, I'd imagine. That doesn't mean that He won't continue to rule, nor does the end of history mean that the Levites won't continue to minister in a role particular to them.
That's a good point. In the heavenly realm there seem to be certain classes of angels with certain responsibilities. Cherubin for example, and seraphim. There's no reason to think that glorified humans won't have specific roles in eternity.