Carb first, as you stated. Get it set to standard settings. Fresh fuel. Does it rev high at standstill and then slowly drop revs until it dies unless you blip the throttle? If so then the left hand crank seal could be shot. The technique for testing this is the same as you used for testing any air leaks. Take off the left hand crankcase cover and, with the ending running, spray a little wd40 type fluid behind the spinning rotor. A change in engine speed will mean that the seal is shot.