With respect to the iron theory, when I was prescribed and took iron I no longer had the craving, and actually I was put off the whole idea. I am no longer on iron and am back to eating ice.
I have had pulsatile tinnitus for over 10 years, not ringing per se, but a "whoosing" that gradually gets louder, sometimes interrupting my sleep. The doctor who prescibed the iron suggested that since my hemoglobin was not adequately handling the iron, and my red blood cells were small and misshappen, as the blood courses through my carotid artery it causes a bruit which I hear as a "whoosh". When I was on iron the whoosing actually stopped. Nonetheless, I stopped the iron supplementation, and am back to crushing and enjoying, and dealing with the air in my head!
I hope it helps.