You should verify that the float valve is sealing properly. I mention this since you've noticed the plug was wet which indicates over-fueling. An easy test you can try is to connect a clear fuel line to the carb which can still be attached to the engine or on the bench in the normal, upright position. Fill the float bowl with gas through the clear line which can be viewed (almost to the top). Now all you need to do is watch the level of the gas - does it hold it's level or drop at all? Some carbs will flood into the engine, others will leak out the vent eventually. It can happen very slowly so be patient.