If any of the interested community ends up reading this HN discussion, this is by far the obvious next step. It can even be done on yourself, with just a bit of help from a friend to do the packing, randomization, and storage of "the answer key".

And if you haven't done it yet, do a full nutrient screening, too. Some of the described symptoms sound like normal nutrient deficiencies. Just because you're eating enough of something doesn't mean you're getting enough of it in you. I've got celiac, and prior to my knowing that, my father and I both suffered from massive iron deficiency, and lately we've noticed we've got potassium deficiencies if we don't supplement. (Alas, even after giving up wheat for years, there's both some scientific evidence and our own experiences that suggest celiacs still suffer from nutrient absorption issues.)

(Emphasis on "if". I do not and can not know. If you've done it, great. If you haven't, you really should.)