For deformation, I suggest turning the mesh on in the scene window. That can help pinpoint handles on the puppet that are locking down movement, resulting in the deformation.
I don’t think the Face behavior with webcam gives you the ability to track Y movement but not X movement. You can put a Transform behavior on the head and do it yourself without the web cam, then you could use a MIDI device with a slider to control the head up/down. Just not using the Face behavior to my knowledge. (There are a few strength settings in the Face behavior you can fiddle with.)