A very interesting idea, but I think we're misunderstanding the Habsburg dynasty and Austria. First off, a major victory at Königgrätz (including killing Wilhelm I, Bismarck and Moltke) would be the start of the war, not the end. Austria can demand Silesia, the Rhine and the restoration of Saxony's old border all she wants, but is she in a position to enforce those demands? I don't think so. Once Berlin rejects such outrajous demands, Austria will have to occupy or conquer Silesia and the rest of Saxony, then turn towards Berlin as a way to force the peace they want. Is Austria in a position to do all that though? I truly don't know.
Second, I think we're ignoring that a victorious Austria will look very different from a victorious Prussia. Austria isn't in a position to form a Großdeutschland Empire nor would she necessarily want to. Now I think the border wished mentioned by @Mikestone8 is very accurate and would be the likely demands pushed by Vienna. But the structure of the HRE/Greater Empire would be more federalist rather than Prussian & friends. I'd take a look at the 1863 German Confederation reform proposal (@Westphalian posted it a few years ago:https://www.alternatehistory.com/forum/threads/1863-reform-act-of-the-german-confederation.282068/) as a basis for the reformed state, though with less duelism and more Austrian dominance.
Second, I think we're ignoring that a victorious Austria will look very different from a victorious Prussia. Austria isn't in a position to form a Großdeutschland Empire nor would she necessarily want to. Now I think the border wished mentioned by @Mikestone8 is very accurate and would be the likely demands pushed by Vienna. But the structure of the HRE/Greater Empire would be more federalist rather than Prussian & friends. I'd take a look at the 1863 German Confederation reform proposal (@Westphalian posted it a few years ago:https://www.alternatehistory.com/forum/threads/1863-reform-act-of-the-german-confederation.282068/) as a basis for the reformed state, though with less duelism and more Austrian dominance.