The agitator in your washer consists of two parts: the base and the top part. My question is: the top part of the agitator moves freely in both directions while the base is not moving or the top part moves only clockwise freely?
If it moves freely in both directions then the cam dogs have to be replaced.
You should use the agitator repair kit, part number AP3138838
On the break down diagram bellow you can see the sequence of the agitator part: