I've discovered that the trick is to export using the built-in Blender Renderer instead of Cycles. (As an aside, why on earth the completely internal choice of renderer would make in terms of saving a file to an external standard is beyond me. What the hell, Blender?)
What I've discovered since then is that meshes import okay as 3DS, but textures refuse to work no matter what. Textures now import okay-ish as .OBJ, but it imports the meshes incorrectly, adding extra planes that end up z-fighting. After editing the mesh so that the part that was z-fighting was separate, I'm at least able to "assemble" the meshes in Capture and get them to work. I wish there was some way to improve the handling, but as long as there are workarounds.
Of course Capture is not a CAD program or a 3D modeler, but this makes the ability to accurately import custom meshes and geometry even more important for custom set pieces and the like.
Lars, you gonna be at LDI?