Thanks for the updated version, PerryDS.
I certainly feel you pain, as I see that you have put some work into it.
The Lip-joints are as before, way behind the character. This will not work. I have explored your initial character, checked all 1289 objects; if there is anywhere a negative scale, I couldn’t find one.
As before, I do not see that the rig was build to reset those joints. (E.g., freeze.)
What I find weird, that the Single Skin Object is in the hierarchy. I would disable it. It seems to introduce trouble without any benefit.
What I also don’t understand at all is why the Weight Tag set to 50%, based on the extra Skin Tag? This causes the Head to not be in sync with the Eye-brow. When the lonesome Skin Object is deleted, and the Head Weight is set to 100%, the Head and the Brows are fine. Which leads to confirm the initial suspicion, but a more hidden version of it.
The Brow was correct, the head moved wrongly.
I stick with my suggestion:
… copy the head (just the mesh, no Weight tag, no skin, no texture) into a new project file. Set up the Toon-rig with just the Root, Spine, and Face. Follow the tutorial mentioned above. Then add more if that all worked out perfectly. Eventually just use two first, as suggested in the tutorial, then refine. I suggest this, as this initially weighting will show if those parts work together.
What I also do, when I can’t see the forest for all the trees, I start with a fresh Character object and a sphere, or whatever is simple, and test things. The Toon rig needs some time to master and certainly patience for the first few setups. You will see, if you keep going, you will feel savvier in now time.
All the best