I went looking for answers besides just the clearing the anterior chain improves the posterior chain. I found it in the book I'm reading entitled, "Trigger Points and Muscle Chains In Osteopathy." A great book for your library.
"the lower layer of the gluteus maximus is connected to the vast us externus, which is activated by the same motion pattern. A pull on the vastus externus in addition stabilizes the gluteus maximus.
Always nice to figure out the why to the how. Keep that area free and see how your own hip extension improves.