Soshi Hosoi did write some BGM for the game too, but I don't know if he actually collaborated with S.S.H. on those songs or if S.S.H. just took his work and rearranged it, if that's the level of detail you're looking for. I poked around Hosoi's site a bit and couldn't find any info about that.
It's interesting that on that page for Side-B you found, the info blurb notes that "Wail of soul" here is an arrangement of Hosoi's vocal theme 魂の慟哭 (because it is), but the tracklist only lists S.S.H. for composition. I'm not sure if that bodes well for the accuracy of the credits for tracks 3 & 5 or not.