I wrote a very basic AppleScript, once upon a time, called iPodFolderOpener, which does nothing more than run a basic series of Terminal commands that open up all the invisible folders in the invisible Music folder inside your iPod's invisible iPod_Control folder as Finder windows. This fills your screen with windows. Before you run the script, you make sure you have navigated to the Advanced preferences pane of iTunes's preferences and unchecked "Copy files to iTunes Music folder when adding to library." Then, after running the script, you simply go to the foremost open window, select all, and drag and drop them into iTunes. Go back to the Finder. Close that foremost window, and select the next. Repeat the previous step. Continue doing this until there are no more open windows.
With a large music collection this can take a good half-hour of dragging. It isn't fun, but once you are done, every time you connect your iPod, iTunes will be able to find all those tracks and treat them like any other tracks installed in the Music folder of your iTunes Music Library. You can burn them to CD, reveal their location in the Finder, or copy them to another iPod.
So, If you have set all this up beforehand, like I had, then when you get a new iPod, all you have to do is first plug in the old iPod and let it mount, so that all those files appear as part of the local iTunes Music Folder. Next, attach the brand new iPod and tell iTunes to automatically sync it for you. All the songs in your iTunes Music Library, both the ones on your computer and on your old iPod, will automatically sync to the new iPod. This will be much slower than regular syncing, but you only have to do it once.
Once you are done syncing all of the music to the new iPod, click on it in the side pane, select its preferences from the bottom of the iTunes window, and switch it from Automatic sync to Manual sync.
Now you are all done. Enjoy!