Youre talking out of your behind, Im afraid. The north-south divide is the major cultural fault line in Germany, yes, but thats also true of, say, England. Its just the usual regional variations, nothing more. Divide by religious denomination did not really play a role in 19th century Germany anymore - and besides the Württemberg corelands were protestant, and the Rhineland (in North Germany) as catholic as Bavaria.
All you had, as said, were the usual differences between regional variants found in any nation. There was certainly not a North German and a South German identity, and as Faeelin said economically North Germany and South Germany minus Austria were united in the Zollverein anyway - which also means geopolitical union, because the Zollverein could always also be used as leverage. Bismarck didnt solve the problem by "brute force" - the South WANTED to be part of an united Germany and it already was integrated with the rest of Germany to an important degree (hell, even the German Confederation had provisions to that regard, it was for example incredibly easy to switch citizenships between German states even when they were independent).
As for the three southern states founding an own "counter-Germany": Not likely. Baden and Bavaria greatly disliked each other, and Baden even tried to join the North German Confederation in 1869, even though it was a blatant Prussian dominance setup. Württemberg was never really serious about that stuff, anyway, and while Bavaria was, its finances were devastated. And as said, Prussia could always use the Zollverein as leverage, and then theres also the factor of public pressure on the governments...
Its of course always possible that German (re)unification doesnt happen as relatively smoothly as IOTL, especially in regards to foreign interference - it was really lucky that there was basically none IOTL. Its always possible that the loose German Confedertaion is propped up time after time again by outside powers. However, a stable North-South divide, that is not something that is going to happen.