1) My all-time favorite mori musicians are Popoyans. Their music is just so soft, and magical. It never gets old. I recommend either of their two albums.
(This song is entitled Hoshininaritai.)
2) Another one of my favorite mori musicians is Ichiko Aoba. Her sound is so relaxing and almost ethereal. My favorite of her songs is Hikari no Furusato.
3) One of my favorite mori-esque songs is Honey Jars by Bryan John Appleby. I have never heard any of his other music, and the song's lyrics are a bit sad, but musically it's wonderful. I just can't ever seem to hear it enough, and it never fails to relax me.
4) Another one of my favorite musicians is Jean Ritchie. Her music isn't strictly mori, but she is a folk musician who sings very mori like music. I absolutely love her album Mountain Hearth and Home, and I'd recommend listening to this album to get a good overview of her music.
(This song is entitled Black Waters, and is an original piece about mountaintop removal in the Smoky Mountains.)
5) Last but not least, another one of my favorite musicians is Gungor. They're newer albums are not very mori (although I love them as well), but their first two albums, Beautiful Things and Ghosts Upon the Earth, both have a very mori feel. A few of their newer songs, such as I Am Mountain and Light, also have a mori feel to them, so I'd recommend checking them out too if you like their sound.