A professional who specializes in resolving hypothyroidism, not just manage your symptoms with drugs, would be the best resource to answer your question.
However, I do know that diet, nutrition and lifestyle changes can significantly improve, and in some cases, completely resolve hypothyroidism. I had hypothyroidism with adrenal dysfunction 4 years ago, and I am much better now.
Here are excerpts that discuss evidence-based/research support for diet, nutrition and lifestyle changes for treating hypothyroidism from Dr Douglas Husbands's recently released patient guide to hypothyroidism:
"...specific nutrition, diet and lifestyle changes have been proven to work for hypothyroidism.
According to a large number of research studies, one of the most powerful ... is removing gluten from your diet.
Thyroid disorders from auto-antibodies attacking the thyroid are prevalent in adults with Celiac disease. A 2001 study in the American Journal of Gastroenterology reports there is a high prevalence of thyroid disorders in untreated adult Celiac disease patients and that gluten withdrawal may single-handedly reverse the disease...
One of the most powerful lifestyle factors with strong research support for effectively treating hypothyroidism is to improve xenoestrogen detoxification.
... The bottom line is, with imbalanced detoxification, the cells have less available thyroid hormone...
Research studies confirm that the minerals selenium and zinc are essential in the conversion of T4 to T3. In the form of selenomethionine, selenium is essential to this conversion. For people with severe thyroid problems, supplementing with selenium and zinc and other minerals, is often necessary.
Research suggests that improving T3 cell receptor binding significantly helps alleviate hypothyroidism. The cell nuclear receptors interact with vitamin A, conjugated linoleic acid (CLA), and the omega-3 fats, EPA and DHA.
Rosemary extract has been found to potentiate the effects on vitamin D. Zinc in the form of zinc glycinate promotes proper thyroid function through its role as a cofactor for the thyroid receptor of the cell nucleus. Grass-fed free-range beef is a good food source of CLA. Fish oils are high in EPA and DHA, such as those coming from fatty fish like salmon, which has significant EPA and DHA.
Studies have long confirmed that Iodide provides the nutrient precursors for T4 formation. Iodide is a limiting nutrient in the production of T4. Sea vegetables, such as seaweed, have organic iodide.
Clearly, there is no lack of evidence-based dietary, nutritional, and lifestyle methods that effectively resolves hypothyroidism..."