I imported your model into ue4 and applied the basic material and this is what I got.
Everything seemed to work fine. No weird shading or anything. I checked the mesh in blender and maya and saw some weird geo so I cleaned it up and made it more low poly (you can bake your high res to it) and I also set it up so that you can vertex paint on it if you want. I UVed it and added a second UV set for lightmaps.
Import my mesh and see if it fixes anything. Dropbox - File Deleted
(you might see a small seam down the front of the object if you zoom in. This is caused by the first UV set is mapped.)
Let me know if the new mesh fixes anything.