There is the notion that by treating the thyroid with medication and not addressing the adrenals people tend to initially feel better then symptoms return and fatigue etc sets in again.

It's best to strengthen the adrenals and then the thyroid medication works well. Without strong adrenals the thyroid meds are whipping a dead horse, as they say.

So build up the adrenals with vit C, Pantethine, Zinc, protein etc, take adrenal glandulars if you like but some people do report they are too stimulating. Best to nutritionally give the adrenals what they need to repair.
I know it's easy to read and dismiss but absolute rest, relaxation, a lot of sleep, lots of good food... is essential if you're feeling adrenal burn-out. I slept for 6 months!

Sorry i can't be more use regarding your labs...the morning and night are high so it looks as if something is stressing your system out for you to be producing such high morning cortisol.
Having a high cortisol reading is actually good, in that your adrenals aren't completely burnt-out. Many stressors can cause high cortisol...not just what is known as 'stress' but viruses, moulds, metals and toxins too.

Super high morning cortisol, obviously. I don't think that's sustainable. Remove/avoid stressors, meditate, practice breathing deeply and relaxingly.