I would look at some of the sedges like Carex flacca ‘Blue Zinger’ or Carex pensylvanica. Or better yet, a mix of them. They are all grass like plants and the ones that will work best for you are those that are spreading rather than clumping.
Does the shade come from over hanging trees or is the slope north facing? And what is the soil like when it isn’t wet and sliding into your backyard? And how big an area are you talking about?