My yard slopes down to the street at 20-30% incline. I use wood chips I get from the city or tree trimming services and haven't had any of the mulch slide into the street, even after heavy rains. HTH

Yes, cypress is a good choice for a mulch on a slope. It is more fibrous and sort of knits together. I used it around a pond area and it did not blow into the pond or erode. I feel it is easier to change your future plantings with a wood mulch rather than rock mulch. Its also softer to walk on when barefoot. The one disadvantage is that it seemed to disappear rather quickly through decomposition and from winter cleanup of the flower beds. The smaller wood chips would work as well. I don't know how cypress and cedar would look where they would join together. I have seen an interesting garden that used various types and colors of mulches in patterns. Of course, the mulch was more of the feature than were the plantings.