A few thoughts

I think knusperli does work well but the amount of improvement you get depend on what JPEG encoder you compare it against.I was able to replicate your result with IM 6.9 .However there is a more modern JPEG encoder(by Thomas Richter) you can use that produces better quality JPEG images(less blocky atefacts).

https://github.com/thorfdbg/libjpeg

I compared JPEG decoder from IM and improved libjpeg from Thomas and added them in a zip.

https://drive.google.com/file/d/1jx1XlbI-wb-1EitvXDbA0kMHqlvkEQ7L/view?usp=sharing

Source Image:
https://drive.google.com/file/d/0B0w_eoSgaBLXOU03eXNfc2RSSE0/view?usp=sharing