I guess this will be OT..
Not very versed in the Iodine field yet (I know it's a real treasure) so apart from Iodine protocol, a possible bit of the puzzle could point towards B12 deficiencies and/or so-called MTHFR mutations (problems metabolizing normal B12 and folic acid). It is a huge ever evolving field that grows fast, but if you wanna dig deep, some googling ("hashimoto"/"autoimmune thyroid" + "mthfr" + "b12" + "methylation") could give you some answers or directions to further examine. MTHFR health issues are by and large managable with diet and supplementation.