AHC: reverse Prussia and Austria vus a vis German Unification

Prussias rise is one of the most significant accidents of history. The result of the Congress of Vienna was very much opposed by the King; the Rhineland was distant and filled with cqthilics, and the Prussian would have sooner taken Saxony or even more of Poland.

Essentially I'm wondering if it would be possible to reverse Prussia and Austria positions, that is- make a Prussia-Poland union become a dual monarchy while Austria, after losing Hungary and gaining the Rhineland, eventually forms Germany. I guess the easiest PoD would be to have the Hohemzollerns become catholic, but that has to go back to the Great Elector, unless one posits a successor becoming king of Poland in the early 17th century. As Prussia was predominately Lutheran and the Hohenzollerns Calvinist following the Great Elector's exile in the Netherlands I have some difficulty seeing this come about, but stranger things have happened.
 
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