..and Dynastic Hero,
AFAIK, Nick Wood did personally compose the music for Gate of Thunder and Dynastic Hero (and the animation picture Tōi Umi kara Kita Coo, which sounds a lot like the latter). Dynastic Hero and Coo were co-composed with Julian Lennon.Japanese developers are not consistent when it comes to game credits. In many games, you'll find the composer listed under the simple title "Sound" which could mean anything. In the case of GoT, "Sound Design" was probably a joke on the fact that Nick Wood's studio was named Syn Sound Design at the time. Nowadays, it's Syn Entertainment. The site is in reconstruction, but a few years ago you could find GoT listed in his resume.You can certainly contact him on his blog and ask him for details.
Adding PCE console specific layer on top of that, makes for an interesting challenge (no, not a reference to Ys II).
There's an anecdote about SYN. The name was chosen after the three founders of the studio: Simon Le Bon, Yasmin Parvaneh and Nick Wood. Some sites state that it was founded in 1998, which is erroneous. Syn Sound Design had been in existence as early as 1989.