That would be Großösterreich, ie the Schwarzenberg plan.
You just need a much more stubborn and deluded Prussian court that believes it can actually win if the German Autumn Crisis of 1850 leads to war. So when Bavarian troops enter Hesse-Cassel, the Prussians decide to fight. In that period, Prussia will be beaten down by an Austrian, Federal-German and Russian intervention. The UK would not intervene, and it comes down to the question what France will do.
President Bonaparte has already offered his support for Prussia if he gets the Bavarian Palatinate as compensation, but Prussia has declined. The Prussian role was, after all, the pretend-champion of the (extremely watered down) German Parliament against the Austrian-led monarchical Confederal Diet. Selling a German province to France in exchange for military support would look very bad.
Perhaps that is the PoD. Prussia/FW4/Radowitz ignores public opinion, has a secret agreement with France and feels secure enough to carry on against Bavaria. I have the strong suspision that France would not honor that agreement to the degree our deluded Prussians would hope for. The French Republic of 1850 is not yet the French Empire of 1854 and the power projection of Austria and Russia combined into Central germany is too strong.
When the dust settles, surprisingly few shots have been fired. The UK has acted as mediator. Prussia stays intact beyond come minor losses along the border of Posen (to Russia), Silesia (to Austria) and the Mosel-Saar area (to Bavaria), but it is forced to re-enter the German Confederation, this time under clear Austrian hegemony. Which includes the Austrian
Gesamtstaat.
In other words, this demography: