Weakly reducible Heegaard splittings of Seifert fibered spaces

We prove that for exceptional Seifert manifolds all weakly reducible Heegaard splittings are reducible. This provides the missing case for the Main Theorem in (Moriah and Schultens, to appear). It follows that for all orientable Seifert fibered spaces which fiber over an orientable base space, irreducible Heegaard splittings are either horizontal or vertical.