There is one possibility. DVDShrink is a very good transcoder, equal to any of the commercial choices you can name even though it hasn’t been updated in many years. The free compression program that can beat Shrink’s results is not a transcoder, but rather a front end for one of several different encoders. It is called DVD Rebuilder.
DVDRebuilder comes equipped with two different encoders and a transcoder, all for free. The one you want to use within it is called HCenc. It is one of the best mpeg2 encoders available.
You can find DVD Rebuilder here: http://www.jdobbs.com/Pages/Downloads.htm Use the full installer download at the top of that page.
DVD Rebuilder also has a paid version, DVD Rebuilder Pro, which has more options. But the free version works very well within its built-in limitations. I strongly advise trying the free version for a while to see if it suits your needs.
There is one downside to using DVDRebuilder and HCenc. It is not as fast as DVDShrink, or any transcoder for that matter. If quality is your objective though, this is the compression program of choice.
Personally, I use Shrink on movies that require only a trivial amount of compression. Anything that drops into the 80’s on Shrinks scale (more than 10% compression), I use DVD Rebuilder Pro instead.