"Magnesium and potassium deficiencies have been ruled out."
No, dont think so; magnesium deficiencies does not show up on tests (unless full cell ones). Only symptoms, like cramps show this deficiency.
Calcium does not reduce Iodine effects, but it can help the fluoride detox. I recommend boron instead; as it detox fluoride to some exctent, also regulate the magnesium- calcium.
Magnesium also help detox the fluoride, without it the calcium are rather useless:) Boron is the regulator.