As my helpers stated before, this indeed is an issue with the UVs. It has nothing to do with UE4.
Today I decided to play around with the model in Blender. I tried to merge the different parts into one mesh and import that into the engine. While doing so, I also poked around the material slots and the UVs. What I discovered is, that the complete model (figure 2) was merged while the separate parts had different named UV maps (some even two or three different maps). After a very brief Google Search it turned out, that when merging many meshes into one, you have to match UV map names and make sure there’s only one UV map on each mesh - which wasn’t the case, as I already stated.
What you see on figure 2 is the result of Blender being set to render only one of the two UV maps present on the mesh; the other one is set to not be rendered, which is why it appears the way it does in both Blender and UE4. So by merging the UV maps, the problem was fixed.
TL;DR: UV maps were not merged; merge them into one map and the issue will be fixed.