Of course I exported in 3DS format. If I didn't know how to do that, I wouldn't be using the 3D programs to start with. Their files are scene files anyway, not object files.
I did manage to mostly solve the problem. I realized that any 3DS object exported in Blender can't be imported into NL, so I exported in a different file format (Wavefront .obj) and then imported it, textured it, and then exported it to .3DS with Bryce. This works, but now the objects have no textures.