Cool, a thread discussing one of my preferred causes, Greater Germany.
I agree with Susano that the importance of religious contrasts in the 19th century German politics have been greately exaggerated. The main obstacles to the establishment of an Austrian-led Grossdeutchsland were the political rivalry between Austria and Prussia, the vast extent of non-German territories in the Habsburg Empire, and the reactionary nature of Austrian leadership of the time.
I also agree that the best PoD to create what you seek is in 1848. We need a far-sighted, fairly liberal, and expansionist or German-nationalist Austrian Emperor, who can accept setting up a liberal constitutional monarchy in Austria and administrative divisiion of the Empire as the price to rebuild the HRE as a federal centralized state. Say a PoD that rewrites the personality of Franz Joseph. When the 1848 Revolution comes around, he grants a liberal constitution to Austria and autonomy to non-German areas of Hungary, Croatia, and Galicia under a personal union (an earlier expanded Ausgleich). Austria, Bohemia-Moravia, and Slovenia are set up as a "German Kingdom". A peace is signed with Savoy which cedes Lombardy-Venetia to Sardinia-Piedmont in exchange for an alliance. When the Frankfurt parliament is elected, this causes all German liberal-nationalists but the radical left to rally around the Austrian Emperor to establish a Greater German Empire. Austria supports a liberal revolution in Prussia. The Paulskirche Constitution is voted which establishes the (Greater) German Empire, with an Habsburg hereditary emperor, spanning the territory of the German Confederation plus Prussia and Posen. It is in personal union with the Kingdom of Hungary.
The Empire supports the federal unification of Italy alongside the German model, under the leadership of its new Sardinia-Piedmont ally.
Moreover, France and Russia need to be addressed. France is paralyzed by revolution and political instability up to early 1849, but afterwards it shall most likely attempt to reverse these unifications by war, but the combined forces of Germany, Hungary, and Italy should most likely defeat France. Russia is a more difficult issue: it is not so much geopolitically committed to keep Germany separate as France, but it needs to be countered or placated. A PoD that keeps Russia distracted in 1848-49 would be most helpful to fulfill the scenario: a delayed or anticipated insurrection in Poland, an insurrection in Finland, a war with Sweden or Turkey are all good possibilities. Additionally, its goodwill may be bought by ceding Galicia and Posen, and giving the support of Germany to Russian support in the Balkans and the Middle East.
As an aside note, it is completely false that the centralization of the HRE was impossible after Henry IV. As a matter of fact, one of the best possibilities for an early German unification was during the Hohenstaufen dynasty. You need a somewhat more successful and longeve Frederick I and Henry VI, and a Frederick II raised to think like a German King with possessions in Italy rather than the other way around. By the time this Frederick II dies, he should have brought Germany to a comparable level of centralization as England or France.