I had this problem with my 02 shee. its also stock with pro design foam filter and no snorkel. it would almost never smoke out of the right side pipe. when i would put it in gear and wind it up, it would pop on the right side. a plug test revealed it was lean. after checking air screws, reeds, coil, and putting different carbs on it, nothing worked. i ended up getting an extra left side slide and putting it in backwards in the right side. with the slot facing forward, it slows down the air, therefore it no longer runs lean. i've never heard of anyone doing this, but it worked for me. i saw another post where someone said a leaking cylinder head gasket might cause this, but i dunno.