Extreme changes to mesh deform cage cause problems with shape keys

Most of my meshes require the shape key binding trick detailed by JP Bouza where a shape key is used to fit the object inside the cage before binding since character legs are close together.

However, when the mesh deform cage is rotated via armature in extreme ways, such as upside down or facing the other way, the mesh adopts a very distorted shape that resembles a highly exaggerated version of the binding key. This does not happen to any meshes that are deformed in their binding shape. Dynamic shape keys fix this distortion problem though they also cause the problems that the shape key trick is supposed to solve.

Blend file here with the rig, deform cage, and one mesh with this issue.

https://pasteall.org/blend/9eaf6358a46a408aac7e7c9772b2e29a