Why do you all take for granted that Austria is out of this business?
If you say "united Germany!" in a 1848 context, this implies all German-speaking countries (except those in Switzerland). And that is the whole dilemma.
The Paulskirche Constitution explicitly ruled that a foreign monarch must not obtain a German crown (in one of the German states), and that a German monarch must abdicate before accepting a foreign crown.
Basically, this rules out the possibility of the Austrian Emperor holding at the same time the crowns of Hungary, Croatia, Bohemia etc.
The idea of leaving Austria out of it only came up because of this dilemma, but it didn't really catch on until implemented with force.
So let's think of alternate ways of solving this situation:
One compromise would be that the Austrian Emperor also is crowned German Emperor - but only having transferred the rule over the non-German speaking parts of his Empire to a close relative. Then Austria-Hungary will no longer exist as a single state - at least formally - but be replaced by a close alliance. (This could make the political situation more stable in the long run, but it might as well aggravate the conflict between Czechs, Croatians etc. against the privileged Hungarians.)
But why should Austria consent to such a massive work-over of its internal affairs?
I think you need two ingredients for that:
- Get Austria into some trouble, so that their position is somewhat weaker - preferrably if the unification tends to improve it.
- Grant Austria the leeway so that the split of the Empire is more or less only formal - for instance, in a way that the administration of non-German Austria-Hungary is effectively handled by officials without much involvement of the monarch - and the top-level officials could even be the same as in the German-speaking regions, obeying the orders of the Emperor.
Of course, there is still the question how Prussia (less so, Bavaria and Saxony) will like the idea of being included in an Austrian-led state. No doubt, Austria the the #1 and has a natural claim on a pan-German throne once it exists. But Prussia might hope to better keep her rival in check without the German crown. But perhaps the Empire-split does the trick? After all, it would at least seem a great relief if Austria is formally cut from its Eastern and Southern possessions.