I have the soundtrack, but no longer have the booklet. Unfortunately, the tags that appear on the files themselves don't tell which composers were responsible for what piece of music specifically. It just lists the following for each and every track:
Kenta Nagata, Hajime Wakai, Toru Minegishi, Koji Kondo
From what I've heard, I believe Koji Kondo is only credited here because he created some of the source music themes used in the games, but otherwise he was not involved in the project. I can't back this up, but it's something I've frequently heard. He's just getting credit for original themes.
Unfortunately I can't help beyond this, but if the CDs themselves don't break it up by composer, then the information might not be available. I'm happy to be proven wrong on this though, as I'd like to know myself. I just thought I'd provide what information the actual discs gave.