How to relocate masters and maintain project structure?

I have tens of thousands of images in a hierarchical project structure:

---2014

|---First project

|---Second project

|---etc.

|---Last project

2013

|---First project

|---Second project

|---etc.

|---Last project

2012

|---etc.

etc.

I want to relocate these masters into a directory structure that exactly matches the project structure. Best I can tell, the basic "relocate masters" functionality can only dump images into a single directory. Has anyone written something in Applescript or hit on a clever way to mirror the project structure on the filesystem?

This is obviously in preparation for dumping Aperture.