To give some background, I have taken two ASIs (adrenal stress index) in recent history and both showed slightly depressed cortisol in the AM and slightly depressed melatonin at night.  My naturopathic physician, considered this a mild case of adrenal fatigue (morning cortisol is right at the bottom of the normal range).  Adrenal fatigue is a misnomer; it may more accurately be described as hypothalmic-pituitary adrenal axis dysregulation, which is recognized in the medical literature.

My concern is that if I have lower cortisol in the morning, wouldn't I likely be more parasympathetic not due to a rested state but rather because of depressed adrenal output?

I have been lifting along a 5/3/1 based program and seldomly do additional cardio/HIIT on days in between.  I've just started recording HRV a week before a new cycle after a few weeks break from training.  Interestingly, I've had only two amber days (both from an increased HRV), and my HRV has steadily climbed (roughly 10 pts in two weeks) as I push into the more intense phase of the cycle.

I bought this device to help me better understand if my exercise intensity was too great along with all of my other life stressors, but now I'm concerned that fatigue would appear different in my HRV due to a low adrenal output.

Any thoughts on the matter?  Any ideas would be much appreciated.

One additional thought: I can imagine a diurnal hormonal pattern may simply be due to some skewed zeitgebers. Perhaps I don't get enough morning light, exercise too late in the day or I'm exposed to too much artificial light at night.  I'm uncertain what this information would then say about my HRV related to training but it certainly would skew my HRV.

I'm pretty sure it isn't so much skewing the results as being reflected in your results.  Being in an overtrained or burned out state is typically accompanied by adrenal fatigue.  I would also figure adrenal fatigue would reduce your ability to be in a sympathetic (low HRV) state.  As I understand it, low HRV means something like "rallying to the challenge by short-term means" including but not limited to adrenal output.  If your adrenal output isn't there, then your body doesn't have much of a choice.