We are not very keyed in here on women's hormones, unfortunately, but some things can be extrapolated across genders...
It sounds like your wife has very inconsistent adrenal output...my first guess would be the meds causing this, but I'm not sure the mechanism...another possibility could be a pituitary andemona secreting ACTH, which tells the adrenals to output more cortisol.
The good news is that her adrenals aren't exactly "fatigued" (i.e. unable to produce cortisol) as they seem to be doing a pretty good job of that.
My advice would be to retest and compare the results.
If you can somehow convince a doctor to give an MRI scan for the pituitary, that would rule out the [benign] tumor, but from the sounds of her insurance this might be a non-starter.
A full women's hormone panel from LEF.org or privatemdlabs.com would be beneficial.
How old is your wife?
You said her TSH was "normal" but "normal" does not fly here, especially with TSH as the range is completely fucked up...so what was the value (and range)?
To answer your questions:
It means she is producing plenty of cortisol in the morning. It is surprising she is having such a hard time to wake up with this much cortisol.
The high cortisol could be exhausting her existing thyroid hormones, if they are low, which would leave one feeling tired. My guess is this is what's happening.
The pattern is pretty consistent in MOST people assuming this was a typcial day with typical stressors.
Yes, very much so. They work in feedback to each other, so as one rises, the other should also rise (assuming they are ABLE to rise).
See answer above re: women's hormone panel.
The temperature test is a very good indicator of adrenal and thyroid function.
Take temperature upon waking (before moving too much or stepping foot out of bed). Basal thermometers are the best. Lower temps (around 97, I believe) indicate a potential thyroid problem.
Then measure every 3 more times that day, starting at 3 hours after the first, and every 3 hours afterwards (total of 4 readings spaced 3 hours apart each). Do this for 3-4 days.
Take a look at the fluctuations at each time day by day. High variability indicates cortisol issues (inconsistent output). The temps should also approach 98.6 degrees, otherwise it is indiciatve of low thyroid output. It is not uncommon to see high fluctuations AND low temps, indicating thyroid and cortisol problem.
If that is the problem, then yes. Cortisol is the only hormone we can't live without, so you have to optimize it before treating others. It is possible to treat others and have cortisol correct on its own, but easiest path is to treat cortisol (other items may fall into place afterwards).
But honestly, I think it is probably a thyroid issue or problems with the anxiety meds...