My dentist let me gurgle/flush with sodium thiosulfate during and after Amalgam removal. It binds mercury well. It is not a chelator though, it won't work well inside your body! The difference: chelators have TWO thiol groups that bind the mercury atom from two sides. However, for use in the mouth it is great. And it is dirt cheap and freely available.
Again: it's useless for removal of *internal mercury* (blood and tissues), use it during Amalgam removal.
I'm not saying this will solve all problems, but it should be better than doing nothing (and activated coal probably works a lot worse than this stuff - in the mouth at least).