Everyone seems to be imagining that German national sentiment just didn't exist until the Prussians came along and used it to unify Germany, thus bringing misery and suffering to Europe etcetera etcetera. On the contrary, observe the events of 1813-1815. The Rheinbund was not "Germany", it was the Rheinbund, and anything excluding post-Vienna Prussia can't be Germany. An SGC would imply a NGC, so whether that works depends on whether you consider the Bonn Republic to have been "Germany united without Brandenburg". I don't. It was half of a Germany divided in two. One can have Berlin, Munich, and Vienna polities, but none of them will be Germany and all will feel German national sentiment.
To get an Austrian-style Ausschluss of the actual area of land which is Prussia (Koenigsberg and stuff) would, with an earlier PoD, not be too difficult. Just leave it as a Polish vassal or something. Ausschlussing Brandenburg is a big ask. But anything excluidng Westphalia, the Rhineland, Brandenburg, and a substantial intervening chunk is just not worthy of being called "Germany", and a lot of people will be working for unification.
Originally Prussia didn't want the Western German territory, they wanted Saxony instead (even saying they'd give up their Polish territory for it). The Treaty of Vienna ruined this idea.. Without the Western Territories they don't have any reason to push for German Free Trade or economic unions.
This is a remarkably sweeping statement. Prussia would still be a pretty serious industrial contender with Upper Silesia, Brandenburg, and Saxony. Why wouldn't its capitalists want all the benefits of free trade? It wasn't exactly asthough Baden was a vital artery or inter-Prussian commerce, but it was in the Zollverein by 1835. And of course people are still ignoring German sentiment.
Austria is still more interested in Eastern Europe and the Balkans so they're mostly ignoring the other Germanies.
History does not confirm this hypothesis. The Austrians tried to do everything at once, and nursed ambitions to German hegemony a couple of times. Metternich's Balkan policy was simply "preserve the Ottomans whilst making preparations for their Inevitable Collapse", anyway. Given that the Inevitable Collapse was a figment of European imaginations...
Bavaria, Baden, and Wurttenburg will be a pretty powerful block in the South while Hannover is dominant in the North. They will probably work out an economic agreement and eventually unify.
And why doesn't Prussia sign on, pray?
Well, maybe have the Austro-Prussian war result differently with an eventual true South German Confederacy coming to be to counter the North German Confederation, after that have the North fall apart do to bickering and the minor states not wanting to be ruled by Prussian hegemony, resulting in the ex-NGC states merging with the SGC to form a new German Confederation and eventual Unified Germany while simultaneously keeping Prussia out.
Once again, this "countering" notion makes it sound like the Germans all hate eachother. More local unions is fewer systems to harmonise into a fully united Germany.
As to the NGF collapsing:
1) People wanted German unity. "Prussian domination" was resented but hardly to the extent to seperatism.
2) The NGF was a) Prussia and b) Prussia's Puny Insignifict Vassals Pwhahaha. They have a snowballs chance in hell of steering their own course, even if they wanted to for some reason.