I wonder if Abraham's hypothesis is correct, except that, if an autoimmune disorder is already present, it overreacts to even small increases in thyroid activity.
It makes me wonder if people in your situation might need super high doses of selenium and magnesium on the Iodine protocol to counteract this. Just pure speculation, though.
I hope you can get this fixed! Keep us updated. Your case could be very informative for others in the future.