There are plenty of tests which can show what's wrong with you - but they're not "standard" in the sense of doctors using them.
If your morning cortisol is above a certain level or below a certain level; if your morning, before-you-get-out-bed axillary body temperature is above or below a certain temperature (under 97.8 or above 98.6); if your blood pressure deviates by a certain amount over a 16-hour day; if your average temps deviate by more than 0.2 F from day to day; if you have post-exertional malaise… you have an HPA malfunction of one kind or another.
I'd say "you should also get your thyroid checked" but the blood tests for that are atrociously useless. Check the symptoms. Low body temp, especially in the morning before you get out of bed (mine ranges from 96.5-97.4), slow heart rate if you're not an athlete (mine is 50-60 bpm and I am NOT an athlete!), puffy face/eyes, myxedema (non pitting) swelling/thickened rubbery skin on your upper outer arm or shin, changed ankle-tap reflexes, very cold extremities, Raynaud's phenomenon, etc., those are the signs that are actually diagnostic of a thyroid insufficiency.
These are how doctors have diagnosed and treated low thyroid successfully for a hundred years. The blood tests are a new thing but they aren't very indicative of actual dysfunction (or function).
All of the above is like a lot like low blood pressure. Low blood pressure is only defined by numbers when it becomes dangerous to life. Otherwise, you're diagnosed with low blood pressure if your blood pressure is "normal" or below and you have symptoms. E.g. I have low blood pressure at 100-110/60-70 even though that's considered just fine, because I feel faint when I stand up and other symptoms.
Generally, the best resource I've found is _From Fatigued to Fantastic_. It helped me get much, much, better.
While I agree with most of what you say, the problem is that a lot of studies have been done on the HPA axis and cortisol in CFS/burnout, but there is no agreement. Some studies find low cortisol, others don't. There is definitely HPA axis dysfunction, but nobody can seem to pin it down. I suspect that if you measured cortisol throughout the day and correlated it to a symptom diary and/or a stress test, you might be able to come up with a diagnostic test.
The other issue is that there is no cheap and easy cortisol test like there is for blood glucose. As far as I can tell it would be possible to develop such a test, but nobody has done it yet for a number of reasons (lack of demand, cost, FDA approval, etc).
If someone were to [1] figure out a definitive test for burnout/CFS and [2] develop/patent a home testing kit they would be very rich and help a lot of people into the bargain.
As for Teitelbaum: while he does have some useful stuff to say, he also peddles a lot of quackery.
Re: the contradictory studies… if you go with the group of practitioners who argue that there are different stages to the disorder, they're not contradictory at all. The stages argument says a person starts off with very high cortisol output (because you're under stress) and this is what causes the damage and fall-off of production later:
There are definitive clinical (non-blood) tests for hypothyroid (I mentioned several of them), there are also ways to test for FM/CFS (muscle recovery among others). They just don't get used a lot.
As for quackery -- the only quackery I read in Teitelbaum's book was about the allergy treatment and it's not any more or less quacky than acupuncture (where the research was discredited) so I consider it harmless. Every "canonical" scientist has some kind of nutty side, from Isaac Newton on down the line. (Note: Not comparing Teitelbaum to Newton whatsoever. It's just an ideal, extreme, example.) Everything else in his book is supported with research citations. I've checked them, and others, because I followed his advice.
When you list ranges of temperatures you should indicate the body part that is being tested, because an oral temperature reading will be different than a rectal reading. Also, the temperature readings you gave are slightly inaccurate; this [1] says that the maximum oral healthy early morning temperature is 98.8°F, and 99.9°F overall.
Sorry if I forgot to say: Axillary basal temperature. That is, under the arm, measured for 5-10 minutes, with a glass thermometer or electronic one that'll let you keep measuring that long. If that's higher than 98.6, you really should be evaluated for hyperthyroidism. Doesn't mean you DO have it. It CAN be a healthy temperature. But it's a possible symptom.
If your morning cortisol is above a certain level or below a certain level; if your morning, before-you-get-out-bed axillary body temperature is above or below a certain temperature (under 97.8 or above 98.6); if your blood pressure deviates by a certain amount over a 16-hour day; if your average temps deviate by more than 0.2 F from day to day; if you have post-exertional malaise… you have an HPA malfunction of one kind or another.
I'd say "you should also get your thyroid checked" but the blood tests for that are atrociously useless. Check the symptoms. Low body temp, especially in the morning before you get out of bed (mine ranges from 96.5-97.4), slow heart rate if you're not an athlete (mine is 50-60 bpm and I am NOT an athlete!), puffy face/eyes, myxedema (non pitting) swelling/thickened rubbery skin on your upper outer arm or shin, changed ankle-tap reflexes, very cold extremities, Raynaud's phenomenon, etc., those are the signs that are actually diagnostic of a thyroid insufficiency.
These are how doctors have diagnosed and treated low thyroid successfully for a hundred years. The blood tests are a new thing but they aren't very indicative of actual dysfunction (or function).
All of the above is like a lot like low blood pressure. Low blood pressure is only defined by numbers when it becomes dangerous to life. Otherwise, you're diagnosed with low blood pressure if your blood pressure is "normal" or below and you have symptoms. E.g. I have low blood pressure at 100-110/60-70 even though that's considered just fine, because I feel faint when I stand up and other symptoms.
Generally, the best resource I've found is _From Fatigued to Fantastic_. It helped me get much, much, better.