I looked at the circuit for the timing light I have - it is virtually identical to the photo flash circuit. The main flash capacitor is 2uF. The pickup coil drives the trigger scr gate directly.

In regards to Rogowski coils - this uses two ferrite halves to form a transformer. Since there is a magnetic component it is not a rogowski coil. The other pickup method is to have a wire close to the ignition wire - this works via capacitive pickup.

The LED option sounds interesting. Pity I don't have a suitable led to test it with. I would think the xenon would be superior in terms of light energy though.