Cool. But don't consider Iodine as being a "chelator" by any stretch of the imagination. Chelation requires donation of a free electron pair into the d-orbitals of a metal atom, which is why sulfur and/or nitrogen atoms are present in chelators. (lets neglect other ligands like cyanide and CO, even though it is their lone pairs that are responsible for their acting as among the most powerful chelators)
I don't know but my guess is that when the body has enough iodinated tyrosine species, normal metabolism of HM's is enhanced, perhaps by increase in concentration or activity of glutathione peroxidases and other enzymes.
Offhand, for the halogens I seem to recall that complex stability decreases as one goes down the halogen family and fluoride-metal complexes would be expected to be the most stable, which would make F- an excellent "chelator" if it were proper to consider halides as chelators, but its really not.