It's not a mistake that so many performers are credited to the Fierys. These were such complicated puppets that it took one entire performer to move the head, another to move the arm, etc. All of the performers were then bluescreened out of the shot. You can see them rehearsing in the "Into the Labyrinth" documentary on the DVD.
I can't tell you the names of the other performers, but BoyRaisin is right, Kevin Clash is one of them. Ordinarily Jim didn't want Muppet performers to have the same voices as Creature Shop creations (imagine a realistic creature with Kermit's voice), but Clash was still new to the organization at this point.
The list of singers might be mentioned on the Labyrinth soundtrack CD; if not, the end credits of the movie definitely list all the performers of the Fierys, with the one who does the voices first.
Since this was only for one musical number, none of the characters were given individual names; perhaps (and I'm not positive of this) the Labyrinth CD (or songbook) might also note who's singing what part in the lyrics.