Q: original file cannot be found

Don't do it with preferences. If you copied the entire iTunes folder and all its contents including the vital library file, start iTunes with the option key held down and guide it to the library file on the external.

Have you already deleted the music files on the internal drive?  Since you were seeing broken links I am guessing you probably have, and should not copy the whole folder or else you'll end up erasing all your media files on the external.

You could try just copying the items in the music folder on your internal to the locations they should be in on your external.  In other words, you are trying to reconstruct the structure of your original set of files and folders on the external as if you had done it all in one step originally.

What are the iTunes library files? - http://support.apple.com/kb/HT1660

More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management

iTunes 9: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847

Image of iTunes folder structure Dec. 2011 - https://discussions.apple.com/thread/3547807

see also:

Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/message/13025536

What were your original preference settings in iTunes?  Was iTunes set to organize your music?

I am confused.  It sounded from you initial post that all you did was copy your media files to another drive, then change the preference setting for the location of media files.  While this is not the correct way to do what you wished to accomplish it should not have broken your links since your original files are still where they always were on your internal drive and that's where the library is looking for them even though it is now set in the future to store new media (and only new media) on the external.  The links would only break if you did something such as rename the folder on your computer, or move the files elsewhere.

Read the links I provided above.  See how the iTunes folder is structured  with the library files and the media.  Did your iTunes folder look like this?  It should if you were letting iTunes manage your media.  Cloning the whole folder should not have broken any links.  Cloning would let you start iTunes from the library on either the internal or external drive and see the identical thing (actually it would look identical but you would really be seeing two different libraries that looked the same until you made changes).  I clone all the time and this is how it works.

So, if you are not seeing this, I think there is something that is not getting communicated.  It is possible that you had media outside of the iTunes folder and when you cloned (that was unnecessary by the way, simple copying with Finder would have sufficed) those files did not get copied.  Are all your links broken, or just some? Just some would be an indication that the copying was incomplete.

First, let's see if you can get back to the beginning.  Can you set things back to the way before you started doing all this and get it all to work?  If you can the next step will be to move things properly.

To be honest I am starting to lose track here.  We're up to three iTunes folders now and I'm losing what is where.

A way to get everything that is in the iTunes library into one location is to go to preferences.  Now right now I think you should just aim at getting everything back to "normal" before you start relocating things.  So set everything to default settings which is having the media on your internal drive in the iTunes folder and having iTunes organize your music, etc.  Hopefully once you set it to organize your music and close preferences it will offer to re-organize everything for you.  Have it do that.  Hopefully you will have a copy of everything in your library at the end.  If not, you'll have to go hunting.

Labels/tags are stored at several different levels.  Some are in the files themselves as long as the file can hold tags (mp3, AAC, others).  This includes major ones such as artist, track name, album, etc.  Other tags are only present in the iTunes library.  This includes last played, date added, ratings.  If you remove a file from iTunes and add it again some tags will reappear and other will be re-set.  If tracks are in iTunes and you let iTunes move them about they will not get lost.  If it's a matter of having to add a track again then even if it was in iTunes before it will be as if it had never been in iTunes.

If iTunes is set to organize your media it will put media into a series of folders according to kind, then names etc. -- see the links I provided earlier.  It would be easiest to just copy the top level "iTunes Music" folder to the other drive and everything inside will still be in order.  It's then just a matter of dragging one folder to the other drive.

Depending upon the size of your collection, it will be cumbersome doing a drag and drop backup each time since there will be unnecessary copying taking place.  Probably most of your files will not have changed and there is no point in copying them all again.  This is where it is handy having an incremental backup tool such as Carbon Copy Cloner which will only copy files which have changed.