I've had great success keeping my plate chiller spot clean using enzymatic detergents. They're quite effective while being totally non-agressive against metals. The downside is they're quite expensive but on the other hand you only need a spoonful of it so the cost per-batch is actually quite low. I don't know if you can get your hands on them in the States without buying ten pounds at a time but I think it might be worth looking into it.