Interesting on the CDI, however how do you plan to wire it up, do you have a connector source that matches the CDI plug? It isn't a standard plug that I can think of, at least not for a CDI. I guess you could buy the harness and chop the plug off and splice it into the oem harness, I wouldn't think the harness will match the lengths of your machine quite right, but maybe it will, never know I guess.
If the CDI works when you wiggle it, sounds like bad solder joints for the soldered on plug on the CDI, or worn pins in the plug/harness plug. If you don't mind the cutting and resealing the box, you can open it up and resolder the cracked joints, and I suspect it would work again. Not sure what could be used to re-seal it, maybe scratch it up and epoxy it with some screen reinforcement.
Careful how hot you get it, it has caps inside and around 400-450F they pop (at least they do on a xbox 360). Solder re-flows at something around 360-420F, so the only way to safely fix loose pins is with a solder iron.