Without digging through any other threads you have for background ...
In general, if there is any reason to suspect that there has been iodine deficiency, one should attempt iodine replenishment and throw out sea salt, kosher salt, pink salts, "real salt", Himalayan salts etc.
"elevated antibodies indicative of Hashimotos disease": Also note that when the thyroid has been stressed with higher TSH levels and subjected to a lack of selenium, free radical damage can occur as selenium needing enzymes are not working and tissue damage can occur with possible immune system then detecting normal thyroid tissues as foreign. In this situation when numbers are not so bad, one can restore iodine intake and use a multi-vit that contains 150mcg iodine and 150-200mcg selenium. So one might be able to restore normal thyroid function.
Note that higher iodine dosing does and is expected to increase TSH and then TSH labs are sort of useless. Many doctors with limited knowledge will freak out - needlessly.
I have never seen a report that any doctors have ever asked guys here about their use of iodized salt. Too many have iodine deficiency addressed with thyroid meds. Otherwise, the insane thyroid lab ranges mean that people suffer with "normal" lab results and feel horrible, but docs have anti-depressants for that.