I think we've had a very unsuccessful history of trying to introduce one organism to control another. It usually leads to unintended consequences. Even if that organism is controlled, it typically moves on to the next organism, which would usually be a native species, so I don't think that's a good idea.
They do have native predators in their native range, but they evolved with those over tens of thousands of years. If we were willing to wait tens of thousands of years in the Great Lakes, we would expect they would reach some sort of equilibrium level. As Mr. Sopuck suggested earlier, we know that invasive species go up, and they go down, and they go up. They would level off, but not in a time scale we would find acceptable, nor would we find acceptable the economic impact until that levelling off.