If you are still eating eggs, you haven't quite tried everything. The below is Robb Wolf's autoimmune protocol, you can find in his faq. It means limiting basically every form of lectins and other irritants, so no nightshades, no dairy, no legumes, no grains. (I may be missing something.)
Autoimmunity
Emerging research has
made clear the link between Neolithic
foods (grains, legumes and dairy) and
autoimmune diseases such as Lupus,
Rheumatoid Arthritis, Multiple
Sclerosis and a host of other less
well know conditions. Many people have
found significant improvements in
autoimmune disease by eliminating the
Neolithic foods and building a diet
around nutritious Paleo options. If
you suffer from an autoimmune disease
we highly recommend you start a Paleo
diet and let us know what your results
are. To give your body its best chance
to heal we recommend that you
initially limit the following foods:
Eggs
Tomatoes & eggplants
Peppers, including bell peppers and hot peppers
Spices such as curries, paprika, and
chili powder.
Some of these otherwise
Paleo-friendly foods have been shown
to be problematic in individuals with
autoimmune issues. We recommend you
fully remove not only these foods but
also all Neolithic foods (grains,
breads, potatoes, beans and dairy) for
at least a month to see if they pose a
problem for you.
I'll be honest with you man. Its been the same way for me in a lot of ways. I used to wake up every morning with crippling stomach pain, and going paleo fixed that. Its still gone, but my stomach has been getting a bit worse, or symptoms are becoming more apparent, and I'm pissed haha. I wanted to be done with the stuff.
I've moved on now to eliminating fermentable sugars by eliminating FODMAPs. I don't know if this will be the end, or the fix all, and it probably won't be. Nutrtiion has to grow and shift with us as we move through life.
Also don't lose hope with this initial step back. The body is far more complex than we will ever realize, and perhaps this return of symptoms is a freak accident that will be gone in a month's time. As hard as it is for us to fathom, I'm sure the bodies cycles work just as much daily, as they do weekly, monthly, probably even yearly. Its a chaotic system, there is no predicting it. So lets move with it, and see where it takes us.
(Also a potential hypothesis for the worsening of the symptoms again, is that when you went paleo, your body had the chance to heal. In healing, it started to use up stores of fat-soluble vitamins and minerals. Now you may be depleted in those again, and the body can no longer heal.)
I'm a big believer in the fat soluble vitamins. I think that is our main modern deficiency given the quality of our meat and the lack of organ meats in our diets. You may want to investigate a supplement for Vitamin A (preformed retinyl palmitate), Vitamin D3, Vitamin K2 (as MK-4, menatetrenone), and Vitamin E (as tocopherols and tocotrienols). I take a fermented cod liver oil/butter oil blend from green pastures, but I'm not sure if there would be potential irritants for an autoimmune disease.
Doing some quick research there does seem to be correlation between vitamin d receptor polymorphisms and Hashimoto's. Hashimoto's seems to affect the body's innate processing of vitamin D. Some suggest it could be harmful, others that it could help. From what I've read on the synergistic effects of the fat-soluble vitamins, just taking one can be detrimental, but taking them all together will usually be helpful. Take this with a grain of salt. I have absolutely no qualifications other than a hobbyist. I would try the dietary approach first. Fat-soluble vitamins will boost the immune system and this may be the exact opposite of what you want to happen.
Also be careful about supplementing iodine. From what I've read, its a mixed bag. Sometimes it can exacerbate Hashimoto's, other times it can help. I assume you are already getting regular blood tests, and if not, you may want to start that, especially if you experiment with supplementation.
I wish you luck. I'll probably keep poking around in this area, and I'll come back here if I come up with anything.