Here's an idea...
You have an HPR rocket as the payload of a weather balloon. You have
it hanging motor-down and you have a ballast weight attached to the
bottom of the rocket. At 100k' the balloon breaks and the rocket
disconnects and starts to fall tail first due to the ballast. You
light the motor and it burns the strings holding the ballast and the
ballast drops away. The rocket starts thrust at 100k' in very, very
thin air. Drag should be very low and it will fly much farther than
from the ground.
If one assumes the rocket would go to 17k' from the ground, how high
would it go if launched from 100k'?
Ever heard of anyone doing this?