I would be careful of trying to do too much at once. You don't want to overload your system with anti-fungals and heavy metals. I think it would be better to take a break from killing yeast while you're chelating and vice versa. Keep the diet throughout.
Another good reason to do one or the other and not both is then it's easier to tell what is causing what reaction. If you react badly to or improve because of your chelating agents, it would be easier to tell.