herofan,
There are several things you can do to stop the hay from balling up in the wheel rake when the grass is thick. One is you can widen the "throat" of the rake a bit. Also you can just slightly raise the rake so that the first set of wheels (or two) are raised a little bit off the ground. Doing this, plan on going back for a second round to clean up what you missed. Lastly, you can lock one side of the rake up and only use one side. I hate this method but have done it in a pinch.
By doing these things you can reduce the amount of hay entering the rake for the first lap, until you get to the second lap and you can simply rake with a portion of the rake on the hay and thereby reduce the windrow a bit and lessen the balling.
We have a H & S 12 wheel rake. Only thing I don't like about it is it doesnt' have a center wheel. The next rake I buy will have a center wheel.