Paleo/Primal, all the way. Robb Wolf (robbwolf.com) is an excellent resource and it seems like every week on his podcast there is a question on the air relevant to Hypothyroid and Hashimoto's Disease (typically followed by a praise for his philosophy), and the man knows his science on the subject. Check out his podcast and his book, The Paleo Solution Diet. Mark Sisson is another great resource for a similar diet/lifestyle, albeit Wolf seems to know more and address your specific problem. I believe in the 48th Podcast, Robb Wolf talks specifically about T4 and iodine issues one of his listeners was having.
And as usual, consult your doctor before starting anything.