Paul, martingale is not designed to keep the head lower or help to teach a horse to move correctly/in frame. Personally I'd remove it and instead would ask the horse to come on a bit (or at least to the bit in the beginning). I'd also highly recommend to subscribe to Jane Savoie videos (it's free). They are very straight and easy to understand and give the basics. You can google some on youtube too (like half halt and some others).