I have found Wilson's suggestions very helpful, despite my high a.m. cortisol. Although my a.m. was high, they would poop out very early in the day afterwards. The only advice of Dr. Wilson's I don't follow is I do not take any p.m. doses of the adrenal extracts. Otherwise, I would wake up in the middle of the night and/or not be able to fall asleep.
I do not have the thyroid problems you have. I've been tested twice at my request, and I had optimal levels, even at the newer strict ranges. Yet it sounds to me that you would benefit from strengthening your adrenals, at the very least through nutrition, as it sounds like they are in the beginning stages of fatigue.