2 GMF Governor
Enchantress, I have attached drawings of the governor for your engine. Basically, the lever that the cable is hooked to (Regulator Handle) rotates in the housing and is sealed with an o-ring. It is the only external part of this discussion. It is attached to the regulator lever and pulls on two springs which pulls on the governor control lever which ultimately pulls the governor lever that controls the fuel rack of the injection pump. The engine stop lever works directly on the fuel control lever. If the stop cable works smoothly and easily, then the problem probably is in the regulator lever attachment binding on the case, or the lever shaft o-rings binding on the shaft. where they are in the case. You can try to get some light oil (maybe wd-40 to start) on the "regulator handle" shaft where it goes into the case but that is about all you can do without going into the gear case. That requires pulling the injection pump, so it may be good to get a Yanmar mechanic to do that one if light oil doesn't free it up some. Caution on that one is that if the "throttle" sticks open be ready to pull the kill knob to control it.
EDIT Note that if the engine holds a good constant speed in gear and out, then the governor is controlling the fuel rack well and that is probably not sticking/binding. The sticking/binding would be in the case or inside at the interface with the other levers.