I'm still waiting to see if I get any more feedback on the Slovak stemming algorithm, but it seems clear that the "light" stemmer does a good job, and stripping the naj- prefix is helpful. Some implementation details could change (also stripping pod- or changing the order of stripping prefixes to be before or after the other inflectional suffixes), but the basic set up is clear.
So, the next step is add Elasticsearch plugin based on the stemmer to search/extra (which is license-compatible) and test that out as part of an analysis chain.