I'm surprised I'm saying this, but all that about H sounds good. Maybe you should give him the chance he asks for.
When my son had the lice, I took him for a buzz cut after the shampoo. He really liked it. It was my hair and my daughter's that was hard to deal with. I had to go to a good friend to have my scalp checked all the time. Just the thought of lice made me itch! I kept my daughter's hair in tight braids for a long time after that.