Best way around this UV problem?

Here’s how I’d unwrap it if I wasn’t using tiling textures. The green lines are seams, the different colored parts are different UV islands.

Download FBX of the 3d model: https://drive.google.com/file/d/0B7m3EkWf1vh6RUpUazJCS1lPdlU/view?usp=sharing

And the model in UE4 with a quick auto-generated texture.