Hi Susan,
I'm glad you like the new site. Valerie really went the extra mile here.
One would need to have a significant selenium deficiency and also an iodine deficiency for selenium supplements to affect T4 conversion into T3. Even then, the dose would have to be higher than the recommended 200 mcg daily for this to occur. With the average American diet providing 300-700 mcg iodine daily, and the minimum daily requirement being 75-150 mcg daily, iodine deficiency isn't a problem. Also, iodine in excess of 150 mcg daily can trigger and worsen autoimmune thyroid disorders. If your multivitamin provides 200 mcg daily, I'd just take that.
It's true that you wouldn't need another TSI until you're close to remission. If there was a question whether you were responding to meds or not, a TSI could be helpful but this doesn't seem to be the case.
It might be helpful if your FT4 was a tad bit higher. Although an FT4 of 1.2 is within range, for some people this level could be too low for their body's needs. Low thyroid hormone levels can trigger and worsen TED. You could ask your endo about lowering your methimazole dose to 3.75 mg daily or you could reduce the amount of goitrogens you're consuming if you think they might be contributing.
Muscle pain in Graves' disease is often related to the low CoQ10 levels typically seen. Hyperthyroidism causes lower CoQ10 levels than any other medical condition. A 60 mg daily supplement could help with both the muscle pain and your TED.
Your supplements shouldn't interfere with your methimazole although it's always best to take any supplements at least 2 hours apart from your methimazole dose. Iodine is the only supplement that directly interferes--it works against methimazole since part of methimazole's action is reducing iodine absorption. Best, Elaine