Equirectangular environment maps are internally converted to cube maps because only this format (and cubeUV) are supported by the shaders. The internal conversion process uses a cube render target with a fixed size computation:
This produces a cube map size of 1024x1024 which is the same as your original panorama
Do you mind sharing a second fiddle that creates the background with these images? It would be interesting to see the difference between both fiddles.
BTW: I think the background in the fiddle already looks quite good.