I can’t tell from your description if the hormone variations are seasonal. There is some research showing that thyroid hormones vary over the year, perhaps affected by sunlight or temperature. (There is also an admission of variation over the course of the day–that’s why we should take replacement hormone in the morning.) I certainly understand why you dislike the variations and are tempted by RAI. Keep in mind that some of us suffer from these swings with thyroid replacement, too. They may not be changes in TSH but in how we feel. It is hard to sort out (and easy to be out of sorts-LOL).