The more I think about this issue, the more I think there's an issue internal to the governor assembly.
To increase engine speed, the throttle cable pulls on the lever ( #15) which increase tension on the spring ( #11 )
The more spring tension, the harder it is for the governor flyweights to push the governor linkage arm ( #10 ) down to decrease fuel flow thereby resulting in the governor maintaining at a higher RPM, the more the cable is pulled out.
In your case, the cable is fully pushed in, putting minimal tension on the spring, so the governor should have no problem pushing down on the linkage and overcoming the spring tension to keep the engine at a low RPM.
At startup there is no force applied by the governor so the spring pulls the governor linkage and throttle lever all the way open to the full throttle position.
As soon as the motor starts, your governor is making some attempt to close the throttle down, but it doesn't seem to be trying very hard and you are able to manually push it down to lower engine speed.
Also, that bouncing around that is going on with the linkage is completely abnormal. Unless the engine RPM is fluctuating wildly and rapidly, the governor arm and linkage should move slowly and steady with no violent bouncing and no sudden movements.
Normally if you were to try lifting the governor arm ( #10 ) upward at the tip, the governor will fight you very hard and immediately push back at you.
I'm not sure if you can even test that because the machine goes to full RPM so quickly.
You can try it and see what happens, maybe it will point us in the right direction.
Maybe try manually lowering the RPM, hold it steady for a bit, then rev it up quickly by lifting the linkage and see if the governor tries to fight back at all.