It does all sound like FM..and it likely is. M0rie is right about it working.
I kind'a figured (read: Thought up out of the clear blue sky) that the flux field would get a 'dent' in it as it spun past the larger lighting coil, and the 'rebound' of the field would happen just about the time it flew past the ignition excitor.
There are flywheels (like RickyStator's Banshee piece) that have stronger magnets in them for increased output. He uses them in conjuntion with his 200W (OMGosh!) Banshee lighting kit. Like some dual sport jobs, that stator has multiple coils, counterwound in succession to get a higher wattage output.
I've not seen a KDX flywheel with that setup. Not likely anyone would bother with making one. Who rides a KDX these days anyway?
Sort of like 3-phase AC compared to single phase. Same voltage output from each coil but those outputs are stacked next to each other. The load doesn't get the chance to decay the supply before it's smacked again with another sine wave.
How about a couple of those little 1-farad caps patched in. Wonder how that would work.....
Here's another BTW for 'ya. Gap your plug a bit wide. You can feel the difference between .026-8" and a healthy .030". I haven't tried that with an ES, but the EG handles it fine.
..when your bike gets hard to start..check that plug to make sure it's not grown to .035"! THAT will tucker you out (kciking it)!!
BTW...that engine doesn't have much of a frame wrapped around it. What'cha doing to it?