I have been having the same problem as you have. I have spent months trying to figure it out until today. Some how I got lucky by default, my problem was solved. This is what I did.....
I reformatted my ipod and when it asked me if I wanted to sync music I did NOT click on the box. I actually haven't synced any of my play lists . Instead while my ipod was plugged into itunes I just dragged my play lists up to the ipod icon manually. All of my play lists are displayed however my amazon music went in differently. I did as someone said in one of your threads above. I put my music on a USB and transferred it by dragging the music file from there directly to the ipod icon. Now this music does not show up on my ipod in my play list menu only in my Albums. I have no idea why.
I hope my little miracle will work for you too!
I still have not checked the box in itunes to sync any music.
Indeed deleting the song from iTunes and reloading the track from the current file location worked for me. As I keep all my song files on an external drive I guess I mixed both solutions. The rrot of the roblem in my case was a song bought at Amozon. I have been struggling with the issue for months so thank you all for the tips!!!