Maybe the head tilting to the side results in a posture change that tilts the shoulders and that puts the elbow below the level of the shoulders.
In any case, it sounds to me like you do need to eliminate the head movement and get your pitcher to keep his head upright. Standing next to the pitcher and using your hand to position his head is fine. I believe I've actually done that once or twice before. Another option is to videotape the pitcher from the front or back so he can see the head movement. Many times, pitcers don't think they're really doing what the coach says they're doing. Or, they don't think they're doing it to the extent the coach says. Letting them see themselves can often help them understand what you're seeing and they will often make a big adjustment on their own.
In any case, it will take lots of repetitions to change that habit.