Voxels or similar? What makes much of the 3d requirement so strict is because the polygonal base with requires very strict math.
For examples, have 3D built on basic atomic shapes makes it a lot less prone to the error. An early example is Ballz:
http://www.mobygames.com/game/snes/ballz-3d-fighting-at-its-ballziestThat way you can go dirtier and less exact without everything breaking up.
Another related issue is texturing. If you skip textures and uv-mapping you can be a lot less strict with rules of model building.
When you go with voxels, objects become more like sculptures as they have an inside, and is not the fragile paper-thin representation that polygon meshes are.
All of the above have other problems though of course, but as always there is no perfect way.