You're right in that Satie does span 19th and 20th. But see http://www.af.lu.se/~fogwall/list.html
The Gymnopedies are written and released in 19th century. Others, such as Trois Sarabandes - were written in one century but published in the next.
Also, thanks for the info on the Tchaikovsky and Grieg adaptations by Ellington. I'll try to look for them. Grieg's Peer Gynt is beautiful.