Holy crap. This very much matches my experiences. I'm not military, but I used to shoot air rifles competitively in high school. I was definitely overexposed to lead. I remember my fingers would literally be coated in lead, and I don't remember even once hearing that we should wash our hands after shooting.
My experience with trying to get a medical professional to actually give a shit about the matter is exceptionally frustrating. Every doctor that I've ever spoken to have all come just short of laughing in my face when I try to self diagnose myself, and without exception, try to send me to get blood tests - which give no indication of lead poisoning except in recent exposure. I really just want some closure on this, since I know there's not much I can do treatment wise. Getting a doctor to take it seriously is an uphill battle...