Ah, forget it- found, after very careful inspection, that altough the white cubic plastic connectorhead of the new stator unit seemed securely connected, inside of it it was faulty.

Wasn't visible, I just checked every small wire that was connected to it, and found that I can pull out O_o one of the wires together with the copper end... I fiddled a little with that cheap plastic head, and managed to make it stick.

Now the pickup coil's message is ACTUALLY reaching the CDI, so it DOES produce a spark. ...

I would say sorry, but it wasn't visible at all- had to find it. And also I can't delete the thread :( but maybe someone can benefit from this, as sometimes the secure white plastic connectors ARE defective, and have to play with them to fix them.