KISS
I had a sales manager once who was a firm adherent of the above principle, however it all depends on the ignition lag.
Yesterday ( the 17th ) it was suggested that it might take up to 5 seconds of triggering to get the rocket motor to fully ignite. I am sure I have seen another estimate of approx. 200mSec..
If the latter is nearer the case, then firing on balloon burst becomes practical. Merely mount the main lifting cable on a point designed as a spring loaded switch, open under lift. When the balloon bursts, the spring relaxes, the switch makes, and the motor fires. A back up timer would be a good safety measure.
A night launch is almost certainly out of the question - has anybody seen the regulations for flying a kite at night ?
Simkin, above, makes a good point. Rocket motors are recoiless, upto a point. There is a considerable Sci-Fi literature considering using RPGs etc. in space combat - messy !
I still drink to your success !
Chris Cosgrove