Export Model Textures Per Face
UV mapping assigns fixed positions in the texture to each vertex. You'll have to distort the image so that it maps to a constant area in "model size" so to speak. I found the following other question that will probably give you a solution: https://blender.stackexchange.com/questions/22872/unwrap-uv-map-proportionally-to-object-size

It won't give disjointed parts like in your image, but I think it will still provide what you're looking for.