Resistance values between CDI connections/contact points appear in service manuals, but . . . word-on-the-street, values are elusive; hard to measure effectively with digital ohm-meter. Worth taking a look, still, IMHO.
Substituting a known good CDI might help with diagnosis.
Also, dynamically . . . besides the RESISTANCE of the pickup coil, the OUTPUT is of some concern. You should see a voltage spike with every crankshaft revolution from the pickup coil; again, part substitution may be in order.
You say the stator (exciter?) coils supply voltage to the CDI; what value AC? You're probably aware, the engine kill mechanism (from either the kill switch, or the OFF position of the ignition switch) is GROUNDING (earthing?) this voltage; might check and see if a pesky ground (earth?) has entered the picture here.
We can recommend KLR experts in Arizona, but . . . not sure about in Tombstone, "the town too tough to die!"