Maybe the left float is out of adjustment a letting a bit of fuel flood through the pilot while it's on the sidestand. This assumes you know that the pilot jets are equal sized (but really how likely would it be that they'd be different?)
Can you attach a clear tube to the bowl drain and open it to see how high the fuel level is (shape the tube like a J with the open end above the petcock). That'll tell you if the float is wacky. Generally speaking the fuel level should be +/- 1/8" from the gasket between bowl and carb body.
