Joshua was kind enough to fill in the blanks and provide additional details. Good guesses, guys
I left the composer for the Rage Racer track as unknown.
Mobygames credits Hiroshi Okubo and Tetsukazu Nakanishi as the music composers, but the
Wikipedia says Okubo was just the director, without backing it up.
Also, I contributed with my particular take on the "CLASSIFICATION WARS" :P