I don't know that you can. Mine is testing 8am serum cortisol, which is a near-useless measurement, just to rule out that something isn't horribly wrong with my adrenals. I will be genuinely surprised if my cortisol is anything other than low-normal because I don't have enough adrenal symptoms, only the dizziness.
I just got the Stop the Thyroid Madness book and it has a section on adrenals that you might find helpful. You know about http://www.stopthethyroidmadness.com/ right?
My endo would really like me to see someone who knows autoimmunity, but he says all the rheumatologists at the clinic where he works are only interested in people with joint pain. (Not sure why he's clueless about autoimmunity since Addison's, Hashimoto's, Graves', and Type 1 diabetes are all endocrine diseases.) We talked about the possibility of a neurologist but neither of us think a neurologist would see a deficit in cognitive function without any sort of baseline because I generally test high on that sort of thing.
I found an endocrinologist with really good reviews, who prescribes armour thyroid based on symptoms and labs (not just labs). I am in the process of obtaining all my medical records to bring to that appt. on Monday. I am hoping that helps! Thanks for the link to stop the madness-It has been very helpful!!!