Try this.
Take the air Filter off. Start the engine, and rev it to full throttle, and put your hand firmly over the intake, completely chokeing the engine.
This will create a strong Vaccum, and suck any crap through the jets.
It is not a Governor problem, the fact the governor is working proves that. What is happening is the Engine is running at say 3000 rpms, and it runs lean to the point it cant run any longer and start to slow, thusly, the governor opens the throttle, allowing the carb to draft stronger, and pull more fuel up, it recovers, and closes back down.
Typically, the jets are a little gummed, and causes it to run slightly lean, with todays CARB and EPA laws, they are lean from the factory, so there isnt alot of room to play with before it hunts.
If the governor wasnt working, the engine would run lean, then shut off.
If you run it slightly choked, does the hunting condition go away?