So I was screwing around with
good ol' JASRAC J-WID. Sometimes I just like to punch in some names and see if anything interesting comes out.
It turns out that, at least for some registered tracks, searching for romanized names works just as well as for the Japanese names. So, if I wanted to pull up Nobuko Toda's four tracks on this album, which is registered, I could search for 戸田信子, or I could search for "toda nobuko." It doesn't look like the romanized names are actually displayed anywhere; they only work while searching.
What can we do with this? Well, there are two composers on this album with unknown name readings. Let's see how JASRAC thinks their names are read by taking some guesses~
Track 6: 予選前半戦結果発表 by 西木康智
Track 37: 「クイズマジックアカデミー」より「決勝戦」 by 川島条
I have no idea how reliable the JASRAC name data is. I'd hope it'd be pretty good, since copyright is involved, but maybe the names are autogenerated or something. I couldn't verify Yasutomo Nishiki or Jou Kawashima through anywhere else.