I think I would be able to draw a 3D trajectory using more cameras, but I think the setup would get too complicated, we will see...
Just from geometry, you would only need two cameras, and carefully survey their orientation and relative position. Then check it with reflective markers or something. You also need some sort of a synchronous timing arrangement - it doesn't have to be accurate in absolute terms (I don't recommend GPS) but you need something to keep them the same time base within milliseconds.
If you know any model rocket/"spacemodeling" guys, there have been extensive analyses of a two-station altitude tracking setup that is exactly what you need. Each discrete sample of your cameras gives you and azimuth and elevation vector from the camera to the airplane, from that and knowledge of the camera position and orientation, you can get a position of the airplane in your system's "reference frame" in 3D. That is precisely what model rocket tracking station data reduction does, the difference being they do it once to get a single 3D position fix and then, finally, an absolute altitude reference. You care about is the entire fix, but you also only care about relative to the other fixes you get once per 5 milliseconds, or something. That sounds daunting but with the proper implementation, child's play for it to be done in the 10-ish seconds you have before the next maneuver.
It would be a simple matter to add lens distortion to the system, correct each vector based on where the vector falls in the field of view. Most photographic manipulation software already does this, with data from the lens manufacturer, and it is also sensed by the camera and done on the fly when creating "processed" formats inside the camera.
Once you have that, you can easily generate the track from other viewpoints for coaching purposes.
I also think you will need some sort of targets on the airplane to ensure you never lose track (as it does sometimes in the videos). If it means better coaching or or more accurate scores, you won't have any trouble convincing people to do that, I expect.
Still and all, very good and offers great potential.
Brett