I don't have hashimotos, but according to Brownstein and others here on the forum, you need to make sure you take selenium along with Iodine to help suppress the antibodies. Going gluten free is something that was recently found to be key as well.
Stephanie Buist, thyroid cancer survivor is a patient and friend (and probably at this point colleague) of Dr. Brownstein. Her website http://www.naturalthyroidchoices.com
details her journey with being diagnosed with cancer and going thru radiation and finding Dr. Brownstein who she credits with saving her life. She has a husband and 2 kids with hashimotos. And her husband got his antibodies down with selenium and Iodine (iodoral) the last time I read any of her postings on her Iodine board (at least 2-3 years) her husband wasn't on any thyroid meds (desiccated thyroid preferred).
I guess depending on where you are with hashimotos you may need thyroid meds along with iodine and the companion supplements and of course eliminating gluten from your diet.
You may need pulse dose the iodine (keep taking companion supplements even when you don't do the iodine) while detoxing. Stephanie was quite toxic with the radiation and cancer and spent a couple of years on metamatrix supplement powders and going thru detoxing. She also did coffee enemas. She has an iodine group on yahoo that would be a good source of info. http://health.groups.yahoo.com/group/iodine/
In addition to the companion supplements... boron 15-30mg to help pull the fluoride out of your body should be added to the list.
Also, may be necessary, taking any number of detoxing steps like the liver diet (google the liver doctor), taking supplements like milk thistle, or N-acetyle-cysteine to help the liver detox the bromide, juicing green veggies, doing Liver Cleanses if you are up to it (if you are not familiar with Liver Cleanses it involves downing at least 4 oz of olive oil with equal amount of citrus juice -- lemon, grapefruit, or orange), and Epsom Salts to open up the bile ducts and flush out the gall bladder. Then there are Bowel Cleanses and parasite cleanses, that may or may not be helpful in detoxing your body and suppress the antibodies.
If you are on synthroid, find a doctor who will prescribe desiccated thyroid med like armour or naturethroid.