I would think that the wet plugs are gas fowled not oil fowled. To get them oil fowled as fast as you are stating there would have to be a serious internal issue.
Based on you saying it will start fine and run for a couple of minutes then stall out and not start and have wet fowled plugs I would look at the carb first.
Next check to make sure you don't have fuel over flowing into the carb by removing the plugs in the bowls. The fuel should just barely dribble out when the engine is running. If it's pouring out then the float is stuck, saturated with fuel and sunk or there is a bad needle. You could try adjusting the float again but since this issue came up after sitting and it ran fine before an adjustment is likely only going to be a temporary fix even if it works.
