Idiopathic-you sound like me a little. I have tried, but never commit, because I don't have a diagnosis yet for my PN.
Also, had the blood test done for Celiac and it was negative, but some will argue that the only true way to test is from a biopsy of the tissue itself. We just can't trust these blood tests in general, can we! Everyone you ask has a different answer !! B12 in particular has many variables, like the ranges considered normal, and intrinsic factor,

Anyway, I think for anyone with idiopathic p.n, it is always worth a shot to cut out gluten for as long as possible, then re introduce and note any symptoms.

Another thing I wanted to ask is if you have ever considered candida ? This is yeast overgrowth. A quick Google search will explain , if you're not familiar. The possible symptoms go on and on. You mentioned brain fog, mood swings and anxiety. I remember these in particular from working at a health food store for years.

Food for thought :-)