I know the type motor you mean. A couple of ideas:
Let the motor just sit there, not running and see if fuel eventually drips from the carb, meaning that the float valve might leak a bit.
Run the motor, let it idle and die on it’s own and look at the plug, to see if it seems more wet or dry.
Make sure the idle exhaust relief holes are nice and clear.
Make doubly sure that the carb is pushed fully onto it’s mounting flange, tight against the o-ring, before the pinch clamp is tightened.
Do you have a manual for it? I think I have one for an identical Mariner unit, someplace. I will check; but if I recall, they are not even supposed to idle below like, 900 RPM or something. Also, are you sure the e-ring on the throttle plunger needle is in the right spot, per a manual?
Beyond that, I am starting to worry about the lower crank seal….
Long live American manufacturing!
