My first thought was IP6 as a great chelator of iron and other minerals; but mostly iron. However, it is not supposed to reach into the red blood cell for this purpose. So that should not cause a high tibc. And I don't even know if you are using this.
Then I thought of iodine, which is a good chelator; but I remember that you are using potassium iodide, which is not a great chelator.
How about vitamin C? Are you ignoring vitamin C? It helps with iron adsorption.