American Standard Cadet 3 - Can't clean!

I have been getting a ring on both of my Cadet 3 toilets just above the water line. It gets to be black with about a quarter inch of orange underneath of it. I have tried "The Works" and American Standard told me to use "CLR". Neither have cleaned the ring completely away. I am wondering if the tank hardware is causing this problem. I have never seen something like it before. Has anyone else been having this problem? Can someone make a recommendation as to how to clean it and keep it clean? Thanks!

Have you tried adding a cup or so of bleach to the water and mixing it up then letting it sit...you could also add a dollop of fabric softner to the water also to allow the bleach to penetrate better...