Were you aware that the music played in the Primeval World section of DLRR is not Disney music? It's actually the theme music from the 1961 movie Mysterious Island from Columbia Pictures, and it features the great special effects work of Ray Harryhausen. I know because I've seen this movie about twenty-five times on TV.
As for other non-Disney music, there is some played at DCA, including The Beach Boys and the Mamas and the Papas (California Dreamin' of course).
Is there any more non-Disney music at the parks?