There is a blog video on their site that goes into the sound of the show. The "band" is on stage a lot, so music is a huge part of the show. The band is actually dressed as either a "Swing Band" or in traditional Indian garb. There is no allusion that this music or the show for that matter is realistic. It is a hyper-fantastical world.
I haven't heard anything other than that video or the demos of the cut songs. The Terry Gilkyson songs are from an earlier version of the movie. Much of that story was darker and more in-tune with the Kipling book. I'm sure she found a home for at least 5 of them! There is a 6th Gilkyson monkey song that seems to be where "I Wanna Be Like You" is. So that one is probably gone.
I haven't heard it mentioned, but much like the Hans Zimmer/Lebo M material, she also has the George Bruns complete score to work with, including a beautiful overture. Some of those leitmotifs might be used to develop new songs.
Richard Sherman saw a workshop I believe but I don't think he was writing anything new. There are two sequel songs from the canon but those are post-story so I doubt they would be used.
Video