What about a highstart like used for launching sailplanes? It would be a two person operation.

Person 1: Hold the jet at end of runway.

Person 2: Streach the highstart and hook it up to the launch hook on the bottom of the jet.

Person 2 (pilot): Throttle-up and give the signal

Person 1: Release

The heavy duty highstarts lannch some fairly heavy sailplanes to up around 500' and all the jet would need is takeoff speed!