How to blend shape key with vertex group, but pre-calculate w/ proximity modifier

I have two shape keys, and I’d like to do partial blending of them based on a vertex group. I see that Blender supports this functionality; so far so good! :yes:

But I’d also like to dynamically change the weights of the vertex group with the Vertex Weight Proximity modifier, thus changing how the shape keys are blended.

I’ve tried this, but it doesn’t seem to even be noticing the Vertex Weight Proximity modifier. Is this due to calculation order (i.e. the shape keys are blended before evaluating the Vertex Weight Proximity modifier), or am I just doing something wrong?

If what I’m trying is not possible, is there any other way to blend two shapes of an object based on a vertex group with dynamically changing weights?