Ok guys, I've got an update. I went ahead and purchased a new Yanmar injection pump as my existing pump suction elbow had failed and was allowing air into the fuel at that point. I'll probably send it off to have it repaired so I can keep a spare on hand. This appears to have solved the issue of allowing air into the fuel line, and the hunting/surging issue...
However, I still seem to be running at higher RPMs and I'm getting weird readings from my multimeter (hz setting attached to 120v output). (What are Weird readings?) My generator hz meter is still pegged when running. This leads me to believe I have an issue with the governor. (What you need to do is establish what you have for a Hertz reading on the gen set output. Then you can decide what to do. Just because the meter is pegged, doesn't mean that the output is to high. And "still seem to be running at higher RPMs" is not proof that it is. ) According to the manual, with the switch in run, the governor lever pointer should be centered. My old pump just had "o c", my new one does have a center mark, and when the governor is in run, the pointer is WELL to the right of center. The only way I am able to get the pointer aligned to the center mark is by extending the adjustment screw on the fuel injection limitation screw well past the specified dimension. I would appreciate if someone could open their access cover and post a picture of where their pointer sits both at run and at stop. The manual just states that if the motor is over RPMs to check the internal governor for damage. I had a thought that replacing the springs on the governor might work, and I will try that with some springs I have sitting around, but if there is an internal governor issue, I will have to dig into the motor deeper.