These briggs 2 strokes like to be worked hard and run at 50:1 fuel ratio If you run them at 25.1 and the motor is not under load they tend to smoke a bit. I am a contractor and run the same engine on a granberg base. It only gives a slight puff of smoke when cold. Anyway my point is I found the easiest way to clean carbon from this muffler is to burn it out.
The trick is to heat with a gas blow torch inside the muffler until the carbon is glowing red.
You then apply compressed air to the red hot carbon and take the blow torch away. The carbon will continue to burn away so long as you keep the air on it. Do this to both ends ie the engine port side of muffler and inside the baffle end ie exhaust exit."works a treat"