And it works perfect every time with the OEM ignition installed? Strange, almost like it's getting it's ground thru the ignition which should not be the case. The black wire coming from the stator is the ground needed to complete the start circuit so it should be attached directly to one of the screws in the backplane with the black from the solenoid. The positive just goes thru the start/stop switch and back to the solenoid. You should be able to crank the engine with the CDI removed entirely.
If that was me, I would put a meter on the stator and test it out for broken wires.
Was there any issue previous to all this? Did you tear it down because of another issue? Have you recently made any changes or replaced any components?