So the more I research this online, the more it really does not look like a fuel issue, the more it looks like either some kind of governor issue or an ignition issue.
Assuming that is true, and ignoring the carb for now, what are some ways I can test and diagnose this, other than buying parts. One idea I was told was to put the spark plug tester on there and run it and see if the intensity of the spark in the tester corresponds to the surging of the motor, and that that can indicate a bad coil. I like that and I'll have to try that.
It still surges somewhat when I pull on the governor spring so that suggests the spring isn't the problem. I want to try firmly holding the throttle open more and seeing what happens. Its the governor causing the problem or reacting to the problem.
Aside from the external spring, I'm not sure what I'd even be looking for for a "bad" governor. I assume I'd have to remove the motor and crack it open, which I have done before on a different machine but I really don't want to do now on this machine. I really want the problem to just be the ignition coil so I could just bolt a new one on and be done