Hello - I have overactive thyroid and in the beginning was subject to a 2-month thyroid storm before doctors thought to check my thyroid level. (That's how it was discovered).
I am puzzled about your docs prescribing Levothyroxine and Levothyronine as I thought they were to treat low thyroid levels. (I might be wrong on this.)
I was prescribed propylthiouracil (abbrev. PTU), and it controlled my levels since the beginning. I also would think that iodine would be bad for overactive thyroid.
I will try to re-read your entry in a day or two when I have more time. It was very interesting, and your situation seems pretty complex to me. I might learn something or maybe think of something that would be helpful for you. My mother had overactive thyroid when she was young, had her thyroid zapped with radiation, I believe. So she is on medication for life (she's 91 now).
Best wishes to you ..... Courtney