Thanks for the quick reply! Maybe they just composed it as Salamander Factory, seeing as the composers you mentioned all are part of that unit (I think that's also what's written in the parenthesis after their names in the youtube video you linked)?
Their discography lists the game under 2003, but the date (3.27) is the release of the game in Japan, and not the release of the soundtrack (5.21). Can't read the information, but using a translator I get something the likes of "four of us were in charge of the sound", as opposed to three in the game credits. Well, I don't know, maybe I'll have to buy the CD to find out, although I'd rather not, seeing as the soundtrack is apparently pretty much a bunch of crap, with short songs that don't loop and furthermore all fade in and out.