So I’ve played around your material and found out what the issue is. Texture projects fine while the mesh is facing X or –X direction. When I rotate the mesh — texture gets distorted. Texture stretches if rotating the object after simulation is being started as well. Moreover, I’ve tested this material with the starter content simple objects and I ended up with the same issue so there’s nothing wrong with my mesh I believe. Scale parameter doesn’t help unfortunately.
I believe you will get the same stretching if you try rotating your object.
Facing X
Rotated by 30
Rotated by 60
Rotated by 90
As you can see while rotating the object texture starts fading out and instead of perfectly applied image I start getting the stretched one. That’s weird.