How can I scale these objects without breaking their relationships?

Question

I have this setup:

1. Duplicate part of a big mesh, and separate it into a new object
2. Hook each vertex of the new object to an empty
3. Parent each empty to the corresponding vertex of the original mesh

Now if the base mesh is deformed (shape key, cloth sim, etc.), the separated object follows it.

Now I've realized that my model is too large, so I'd like to scale everything down, but I can't get it quite right:

How can I apply a scale without breaking the setup?

Answer 1

Instead of CtrlA->Apply Scale, I needed CtrlA->Scale to Deltas.