I've done two rooms in my own house. In the home theatre, I built a wall on each side of 2x4 frames and filled the interstices with playground sand. Same for the ceiling. It was highly successful.
For the purpose built music room I used Quietrock 545, which is a 5 layer drywall with a sheet metal core. Far easier to build, but not as effective. Still, good enough for the purpose and my usual listening levels.
You want two things: first, you want the walls to be stiff so that they do not flex and interfere with the music. Second, you want to prevent sound from escaping. The two goals can both be met, but they require considerations like my solutions.
As for a terrible room, you can always change the dimensions. The scientific work has been done by the famous acoustician Cox, who published the results about 20 years ago. The research is on the website of the School of Acoustics at the University of Salford, UK. As for construction, the people at Quietrock are very, very helpful. Also, there was a reasonably good article published about 6 years ago in Stereophile or Absolute Sound, can't remember which.
Good luck - glad your client had the good sense to hire someone like yourself.