The way I see it your not just trying to keep the surrounding rooms quiet but also the shower itself. Those sterling showers are very noisy for the person taking the shower. Nothing you install on the other side of the wall is going to help that. You need to fill that space with insulation or your basically building a drum and the sound is going to be directed toward the person in the shower.
My final advice is to insulate all the voids around the tub and walls and then install 2 layers of drywall. The two layers of drywall is all the "extra" I would consider. Insulation is standard to me and not extra with a sterling unit.
I've installed over 50 of them over the years and have only had a noise complaint when insulation was not used. also the people living in the house has to be considered,some people can hear a clock ticking from the next room and other you have to scream at for them to hear you.
For a shower your going to have high frequency sound.....high frequency sound is easy to control with common materials. Low frequency will pass through some materials like its not even there.