These motors are a little outside my wheelhouse. With bikes, I've worked with magneto ignition, mostly. Rpm-dependent + load independent sounds like lack of voltage, at the plug. I'd definitely try a new plug, you've got someone Else's experience and that's the easiest ignition test going. While you're at it, ground the plug against the engine, while cranking it over (via the kickstarter); you should see a nice blue-white spark, jumping across the electrodes. Usually...but not always...a fouled plug, with healthy ignition, will have the spark jumping elsewhere. Similarly, a fat-n-snappy spark usually means that everything in the ignition circuit is healthy, including the condenser. The operative word, here, is usually. As rpm increases, there's less time to saturate the coil and condenser. That leaves battery voltage, the point contacts, and condenser health as the remaining variables.
If you've got a voltmeter, check the battery voltage, too. With a battery ignition, battery voltage matters. The only practical way, for most of us, to test a condenser is by throwing a new replacement at the problem.