I've thought about the same thing...
My range is a small outdoor place. Because it's part of a right-of-way for ConEd, it can't be bought out and developed on. Range has a 99 year lease with ConEd. However it abuts a lot of VERY expensive homes, and for noise reasons we can't shoot any pistol heavier than .357, nor can we fire .223, 7.62x39, etc...
I've thought about making something like this, either to "donate" to the range, or something portable that I could take with me.
As far as the BATFE, I imagine that their main issues with sound reduction devices are attachability and man-portability. *Hopefully*, a largeish box or pipe that can't be attached or readily concealed about the person would be exempt.