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My understanding of sound is limited. But I think you have a huge advantage in that you're trying to muffle a very particular sound, rather than prevent contamination from a wide range of possible sources. If you were setting up a recording studio, you wouldn't want to hear anything other than the sound you're trying to record, so you need to be able to muffle the high pitched whine of a FBI drone just as well as the thumping bass of a car driving by, or the trucks downshifting on the highway, etc.
Sound conducts through materials differently depending -- and here's where I'm going out onto a limb -- on how the wavelength of the sound interacts with the density and thickness of the material. Blacksmithing, I imagine, falls within a fairly narrow range of tones, which might allow you to tailor your choice of soundproofing material more specifically than someone setting up a recording studio.
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