Kohler is a bad example to choose as they used two different governor setting procedures, one of which contradicted the “ usual”system found on most other engines.
On most engines one slackens the the clamp screw between the governor spindle and arm, manually moves the throttle spindle to full speed, turns the governor spindle in the direction that would fully open the throttle, and then does up the clamp.
That is the exact opposite to what you have described but is, I believe, correct for your Honda.