How to split a mesh based on surfaces used to make it?

I had a polysufrace. I made a mesh from it with the MeshMachine. Now I’m truing to split that mash into pieces based on the surfaces of the original polysurface. Preferably the split should not cut any vertices in half and just sort them along the seam.

Here my take on it which does not work. It identifies crease on the mesh correctly, but does not split by it.
What am I missing? (313.5 KB)