Why would the chute not be in a tube within the body?
I have never thought of (prior to deployment) a chute package as being very aerodynamic. As a general rule, I have -- for a
long time -- believed that the air should be "opened" smoothly at the front of a vehicle, and "closed" smoothly behind the vehicle. A great example of both would be the Carbinite car as built by Rob Freyvogel. I think that its tail end may have been
a relatively small spherical ball that was used to push the vehicle at the start of its run. Not literally a point, but not huge. Regarding a parachute's packaging, it seems to me that it could be contained within a tapered (in order to smoothly close the air behind the vehicle) 3D shape that is similar to a long, thin cone with it's rearward end being the "point" of the cone. If the cone itself is launched, could it not function as a pilot chute, and pull the main chute into the airstream behind the vehicle? The cone could be replaced as necessary, if it is damaged from abrasion during the slowing-down portion of a run.