mikeandrosalyn said:
...echo chamber in there.
insulation in wikipedia will tell you that there are no magic solutions in sound insulation.
Varying your materials is a good tactic. Some materials block some types of sounds, other materials block others. Do not double up two layers of the same product, that creates a reverberation point so some sounds get amplified instead of reduced.
Density is one good starting point. That is a part of the reason why cast iron drains make little noise.
Trapped air in certain configurations is another good starting point. Open-cell foam blocks sound transfer, but closed-cell foam carries sound through its cells and transfers the sound along to the next cell. Some intrawall insulation batts are sold for both heat/cold as well as sound insulation. E.g. Roxul batts.
I guess you have to open one wall. Use 5/8" fire rated drywall to rebuild it. That stuff is several times denser than regular sheetrock.
Seal the pipe everywhere. Any gap will carry a lot of sound. Think of it like a gap in an exterior wall when you want to prevent air from leaking into the house during a storm. There has to be at least one layer of something airtight, so you cannot rely on just the fluffy kind of insulation.
Summary: plan for a multi layered approach, extremely well executed. Include at least one airtight layer, one dense material, and one airfluff layer.
david