I had somewhat similar situation with my skeletal mesh in 5.3. I had a properly functioning static mesh asset but after making it a skeletal mesh the materials were not applying correctly (like rings with solid greenish color on your third screenshot).
I tried changing normal import method but it didn’t help, then I figured that my specific problem was mesh related: when I was preparing a mesh in Blender I made a join operation (Ctrl+J) and it absolutely screwed all the materials and the way they respect UVs. So in my case it was a prep mistake, I used parenting to attach my mesh to a null instead of joining and after that materials applied correctly.