Not a complete solution to your problem even if it works, but I assume you've tried DoubleTwist? If DoubleTwist doesn't work, you might want to look at iSyncr from the Market.
Both can put playlists on the Droid from what I understand, but I'm not sure if either can import native playlists from the Droid. (I haven't used either of them -- this is just from what I've read on the forums.)
If all you want is to move songs around on a playlist, you can do that on the Droid by pressing down on the left hand side of the song title where the lines are, then moving the song line to where you want it.