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.
You stated it has a manual choke. Is the cable still connected and actually opening the choke when you push it in?
