CATI et al,
I find the embouchure problem you describe to be the most common with which I have dealt in 2 decades of teaching. Bill Pfund, my teacher in doctoral school, called it "the peach-pit chin" because the chin looks like a peach pit. You are correct: the bunched chin renders those muscles ineffective. Moreover, it most often results from (or is caused by) the corners pulling back or smiling excessively.
I find that the following remedy works well for this problem:
1. Buzz long tones (start with 4 beats; add more as strength improves) on the mouthpiece and in front of a mirror. Keep chin flat (or down.)
2. Again on the mouthpiece, make a "siren" sound. As you ascend, focus the corners to the center of the embouchure. This is more of a perception issue than a reality. The tendency is for the corners to stretch as you ascend. You want to resist that trend.
3. Once you can do both of those exercises with relative success, try buzzing a scale up and down on the mouthpiece.
4. Then play simple melodies (like Getchell or the easier Concone).
It is most important to rest frequently in this process. You have muscles that are not used to being involved. They will become somewhat sore. You must give them refresh time.
The chin acts a s a counterbalance to the corners. If the muscles therein don't work well, the embouchure will be unstable.
Let me know if you need more info.