Are you getting enough calories? I struggled with sleep and other issues when I first started trying different diets to improve my health, even Peat style. In my experience, when I consciously started limiting certain foods (Pufa, Wheat, etc) my calories drastically dropped. There's not many things more stressful to the human body than being in a constant caloric deficit even pufa, wheat, or insert any dieatary evil you want. All my issues resolved when calories increased which for me was somewhere around 2800 cals.