After writing this, I emailed Nettwerk about the essentially broken CDs they were selling. Very quickly, they said they could send me a non-copy-controlled one. And a week later, it arrived. I now have happy CD players, happy MP3 players, and a happy me, ‘cos it’s a good album.
Someone at Nettwerk hinted to me that they’re dropping copy-controlled CDs because of all the bother. Good.