Spherical Shape Key Influence

Hello, I’m trying to create a shape key controller which has influence on vertices in a spherical area. Vertices within the sphere are influenced by the shape key depending on how close the vertices are to the core of the sphere. I already tried to create this with drivers and empties but it just applies the shape key equally on the mesh. Here’s a .blend file of what I got so far:

Here’s a example video what I want to achieve:

At 39 seconds you can see the sphere morphing the head of the character.

I would have thought one could just use vertex weight proximity, but it doesn’t seem to work with shape keys. Not sure if it’s a bug, or a known limitation.