A thought for you.

The best way to monitor who hits who is to have it measured from the ground. Ground units have no constraints on their size, weight, power requirements etc, and there's no worrying about authentication stuff.

To extend the laser idea, you can use fluorescence. If the two planes have different fluorescent paints and different lasers, the wavelengths of light from the two planes will be distinguishable even as diffused reflections from the ground. A spectrum analyser would do the job quite happily, and yet more happily if it's in a non-visible range where there's less light around.

With radar or a few radio beacons in the extremities of the planes, you could easily do the math to work out where the planes are in relation to each other. The bonus with this thought is that there is no requirement to modify the planes at all. Just give each pilot a button to press, and the computer can do all the timing stuff and calculations.

Sonar would work as an alternative to radar from the ground, and require less expensive equipment. So instead of firing sound at each other, just sit a large ultrasound speaker on the ground, and have it emit radar-type chirps. Sit a few microphones around, and have the computer to do the work again.

The great opportunity you get with this is to allow anybody who wants to turn up and dogfight to do so, without expensive equipment of their own, or the need to have a sufficiently large or powerful plane to do it. With systems that can calculate the positions and orientations of the craft from the ground, there's a fairly easy step up to having a visual display of what's going on.

Bring on the airbot wars.