Shape Key Creases

I’ve struggled with this problem for a while now… so I thought it would be good to upload the actual file.
Basically, I have a mouth rig on the right that opens and closes. When it closes, however, there is a crease, and I would like it to look more like the figure on the left. Any advice? I appreciate any feedback. :wink:

Here is more detail as to what I am trying to accomplish: