In an effort to lower the volume of my 'pede, I wrapped the internals with sound-absorbing foam. I used a sheet of foam that I believe is used to soundproof ducting and furnaces. It is not a very dense foam, and I would like to return sometime in the future to add a denser material to assist. After installing the soundproofing, I noticed a perceivable drop in volume, though it was not as large of a drop as I would have hoped. The foam, however, absorbs high pitches well and the high pitches of the motor are muted and the sound is more bassy than naked internals.
Here is a picture of the soundproofed internals. It can't be seen in the picture, but the other side of the gearbox is also insulated. I would like to include a video, but the difference is less noticeable on video.