A mystery and no mistake. Apparently another (presumably known good) CDI has already been tried.
What baffles me is that it just won't start, rather than, dies when hot. I think I'd still be trying to measure voltage outputs while running and watch how they behave as the temperature rises, Learned the hard way by taking my SWM all the way to Scotland for a speed hill climb at Doune. First run it got halfway then died. Got back down and it started. Did the next run on a cold engine kicking it up after pushing to the start line and still only got 2/3rds of the way.
Then someone in the paddock produced a multimeter and we hooked it up to the stator winding. Sure enough the voltage cold was X but dropped as it warmed up before finally rapidly cutting to zero. From then on I carried a spare rewound item (Bosch originally). What made it worse was that as it died it seemed to put the timing out. Not too bad on a hill but when I was circuit racing it I'm pretty sure it was responsible for a couple of piston meltdowns (air cooled 2T).
Yet the stator is new. I've had old Morinis with rotors needing re-magnetising and difficult to start - though usually in conjunction with poor winding resistence, but how about a long shot?