Removing SSAO isn't solving weird shadows - what now?

I'm cloning a set of pillows and blankets, and they have that weird transparency shadow that some objects have. I recloned the objects and removed the SSAO following Peacemaker's tutorial. I thought it had solved it, but then I noticed these weird ray shadows appearing in between the mesh pieces. I don't know what else I can try to solve this.

I cloned the stacked crates object to make all of these, because I wanted a floor sculpture that didn't have the "view art" option. And I made shadow LODs for all the meshes. I would love to understand this so it wouldn't happen again.

Here are some pictures of before and after removing the SSAO, and the package file for the pillows, which are showing the ray shadows, if anyone could help.