More questions than answers. As Star said, double check the model numbers. 6hp engine will normally not have an oil filter? 13hp engine will normally not have a carb with a primer bulb? What was the part number for the new carbs and were they OEM? You say it is running rich, but not blowing black smoke? What tells you it’s running rich, plug color? Could you have 2-cycle mix instead of raw fuel? Have you blocked off the fuel supply to see if it runs better when the level of fuel drops in the float bowl? Gravity feed or fuel pump? Some where we are not getting the full story on this one, too many questions.