340 Chugging instead of Reving

At one point (with a cheezy timing lite) it appeared to bounce around. Maybe it wasn't the lite.
Multi-strikes confuse most timing lites. You probably need to get a compatible light. The bouncing around is the evidence of incompatibility.
You might try reving it to a higher rpm than the switch-point, and see if the light stabilizes after the switch point. If it does not stabilize, but seems to drop sparks or have extra sparks or the timing marks appear to be jumping all around, that is pointing to a magnetic pick-up that is wired in reverse polarity.
So if you see this above say 3400rpm AND
you do have a magnetic pick-up,
just reverse the polarity and prove that things are normalized.
As for the coil;
CDI systems run better on CDI- compatible coils, sometimes called E-core coils. The CDI box usually pulses a 525volt signal into the coil, then shuts it off.; So a Kettering compatible coil may not know what the heck is going on. A Kettering coil is set up with a near constant battery voltage input and a switched negative side. The Secondary side is designed to step up the 8.5 to 13.8volts input to around 35,000 volts to the plugs. Whereas when you send a pulsed 525 volt signal into it, they don't always respond properly.
The CDI coil, often called an E-core coil, is specifically designed to handle and respond to that signal.