FWIW, I have firsthand experience with the materials you are considering, but with a different purpose.
I have an office in the house we built that is set up as a music studio. The goal was to soundproof it in both directions; don't disturb the rest of the house, and don't let house sounds in to mess up a recording session.
Our solution works wonderfully for both. Staggered stud walls went in first. Insulated with denim-wool insulation (similar to Roxall, etc.), two sheets of 5/8" drywall on the inside walls, with green glue between them as recommended for install.
two things to watch out for. Low frequency vibrations will transfer through the floor; the only way to avoid that is to float the floor, which is non-trivial. Concrete may mitigate that; ours are wood. The other issue is HVAC. Both for noise and dust, the shop system should be completely separate from the home system.
K