When I was starting our free walk her was head down BUT she was on the forehand. So when you as for a free walk you should be doing what you are doing - retaining enough contact that nose is still on or slightly in front of the vertical, head and neck are down BUT horse is marching.
I look for the arch in the neck - no arch means horse is probably on it's forehand. Once we leave the arena she can push her nose out and be on her forehand, but while working I work on maintaining the march.
The giraffe is him loosing his focus. You could try for a slight shouder fore in one direction until X then switch directions - without raising the head - using more (new) outside rein to (new) inside hip.
I also practice a ton of free walk to working walk and back again - so horse stops (eventually
) anticipating since she doesn;t have a clue as to what I'll be asking next.