Cutting out brep and brep projection out of a brep

Hey everyone,

at the moment I try my best to cut out a closed brep and the projection of this brep out of a larger brep (also a closed one). I deconstruct the brep and cut out all faces from the larger brep but unfortunately some faces are not considered in my example.

I have attached my Rhino and GH file. Thanks in advance

cutting_project.3dm (34.4 KB) (1.4 KB)