Some people have posted that they've been able to reverse their hypothyroidism with matching supplements to their needs. Ginagirl is one of the best examples. Reading her posts is an education in itself. I was not able to achieve this, and have to take thyroid hormone. At the very least, you can prime your body to make best use of thyroid hormone, and minimize how much you need to take.
Adrenal and hypothyroid problems can present the same way clinically. Meaning, you need good adrenal function to help thyroid hormone make it into the cells, so if your adrenals are weak and thyroid is still managing, you can still look hypothyroid on the outside. If the adrenal pattern isn't highest in the morning and lowest at night, you have a problem. If it's very high at night, I would guess you might have a problem staying asleep.
I've been wheat & gluten free for well over a year, but especially when I travel I do eat it. My family is very wheat oriented, and as long as I can limit my exposure when with them, I won't fight that battle. I do have to recover a bit, though, when I get home :)