I also suggest focusing on the glove because (1) cleaning up the glove side may clean up the head snap and (2) it just plain needs some work based on what I see in the picture.
What I see in the picture is that the pitcher has pulled his glove back and outside his torso and this has led to early shoulder rotation. The pitcher definitely looks over-rotated given that he hasn’t released the ball yet. This is both a performance and a health issue.
You can find plenty of pictures of pro pitchers who, at release point, have their glove in front of their torso (left to right) as well as out in front with space between glove and chest. Getting to this position would be one goal and this could help clean up the head snap.
But I’d start by making sure he gets to a good equal & opposite position at foot plant because a short front side is a quick front side and that leads to early rotation too.
If you’re in the Phoenix area, I’d be happy to meet to talk in person. Send me a private message if interested.