Using my 3D model, I quickly discovered that the Pi cannot simply fit into the payload tube -- the RCA, HDMI, and 1/8" audio jack all extend well past the 52mm internal diameter. In fact, the model B board itself is slightly too large!
Using my well-worn soldering station, I not-so-carefully amputated the excess components. This approach seems safe, as I have never once used those ports.
(wow, this image is enormous, TODO: crop it to fit in this text better)
With the primary offenders removed, the Pi is still a hair too wide for the payload bay. (TODO: insert picture of attempted fit here!) The payload bay is conveniently made of a flexible plastic, and with gentle pressure, can be deformed elastically into an oval. Now the Pi can fit! The nose cone and body connector tubes restore the two ends of the tube to proper cylinders, and the distortion is barely noticeable from the outside. Inside, the Pi is clamped quite firmly along the two longest edges. (TODO: more images of this fit)