Any idea how to rig this complex mouth?

Ive been using Rigify presets to rig this face, but the presets are too organic in their ability to deform a mesh. I want the character to have a lot of expression hence the need for a rigify preset. But, I also need the mouth to be really stiff and for its movements to be localised, instead of propagating throughout the mesh.

Here’s some images which should illustrate what i need.

Screenshot 2021-08-20 at 16.53.03
Screenshot 2021-08-20 at 16.56.17

Ill also attach a mockup render of the mesh to give you a better idea, ignore the messy deformation lol its fixed now.

Sorry if this reply is too late. For the parts that shouldn’t move, could you just not apply any weights to those areas? And then maybe you can animate the mouth/lips with shape keys or a lattice.