I don't quite have an answer for you but I would like to share my experience. My 8 year old daughter started having dandruff several months ago. It progressively got worse where her dandruff looked white/silvery and didn't really flake. It made her scalp look really ashy. Her hair even started breaking off (not balding) at the part. This was not in one spot. It was all over her scalp. When I washed her hair it would be fine for the first day then the "ashy" looking dandruff would return the next day. It got to the point where the "ashiness" didn't go away at all even with washing. I took her to the doctor. She diagnosed it as eczema and prescribed Ketoconozole shampoo. Didn't work. Took her back to the doctor. She prescribed LCD which is a tar ointment (nasty, stinky, messy). Didn't work. Since I thought it was eczema, I started using natural products on her hair recommended by another member--Aubrey organics poo & conditioner and jojoba oil. It seemed to really work. But just to make sure it wasn't what I didn't want it to be, I took her to a dermatologist who diagnosed her problem (with special glasses) as a scalp fungus aka ringworm aka tinea capitis. The dermatologist said a scalp fungus is often misdiagnosed and as a result can go on for years. The parts will get wider which hers did. He said young children do not have dandruff. He said adults are usually (not always) more immune to the fungus and their bodies can fight it off better than a child. He said it very prominent in the African American community and is extremely easy to pick up.
Just something to consider. Hopefully this will help someone. Good luck finding your solution.