I messed with your Mesh for a little bit this morning trying to solve the issue. Attached you’ll find two images.
The first is a slightly tweaked UV for the lightmap vs the original lightmap.
In this image on the left is the tweaked lightmap (can be seen in the second image) and the right is the original lightmap. You can clearly see that light bleed is happening on the original.
Here in the second image is the original UV for the texture. I did a check to see if there were any overlapping UVs and there were. They are the ones in the top right and left corners. Moving those up I then reimported this into UE4 and set the lightmap resolution at 128. Both meshes in the image above are using a 128 lightmap resolution.
It wouldn’t hurt to make your mesh a little thicker as you’ve indicated you’re doing, but having a properly setup lightmap can do worlds of good as well when it comes to getting the look you want!
If you run into issues or have any questions feel free to ask!