Thyroid regulation should not be according to anti-thyroid autoantibodies or standard serum thyroid testing.
You may need to find an Endo who treats patients more according to their symptoms (look into Dr. Barnes Thyroid protocols-there are a number of doctors who follow his methods and treat thyroid patients more successfully, than conventional endos.)
The elevated antibodies, could be attributed to the use of cosmetics, shampoo and other products who you may not suspect they contain gluten!
Most hypothyroid sufferers have gluten intolerance and don't even know it!
The gluten molecules-mainly from gmo grains- resemble the TPO
(Thyroid Peroxidase - an enzyme necessary for the signalling of Thyroid hormone production as you probably know by now) molecules and thus the immune system in its response against gluten, attacks the TPO in the Thyroid also!
So you must have a complete list of all the "illegal" products, foods and drinks that contain gluten, including the ones listing ingredients disguising the presence of gluten!!!
In regards to Grains/carbs/gluten intolerance:
Look into Gliadin test (urine), by Cyrex labs. They test 12 forms-not just the alpha ordered by most doctors- of gliadins regarding gluten intolerance (not necessarily digestive).
Now they can also test which part of the body is affected!
I hope this helps, but please note that my comments, do not constitute medical advice.
Best wishes.
Niko