The melatonin angle intrigues me as well. I specifically feel better after dark, which is known to trigger melatonin secretion. I may feel less active, true, but a lot of my neurosensory and cognitive issues improve, I'm more relaxed, and able to concentrate more.
As for cortisol, I've had my day time levels checked, and they're within normal range.
But I'm an odd case; I have no body fatigue, do not get PEM, but have all the brain symptoms of CFS. To this day I'm not quite sure what I have to be honest. The only two things that improve my symptoms are alcohol and night time.