This requires kicking the Hungarians into submission, but it can be achieved. As mentioned, you probably need Franz-Joseph to have a personality transplant, though. Or somehow contrive for some extremely influential advisor to set him on this course.
Anyway, this means any reform happens on Austrian terms. As also mentioned, it certainly won't be like the USA. That approach was utterly alien to Austria-Hungary, and probably for the best. The situations are far too different.
You'd probably see Austria directly absorb the German-majority border regions of Hungary. The region of Slovenia (including Trieste and the surrounding coast) would probably also be integrally included in Austria, without much local opposition. The Sudetenland would also become part of Austria proper, but Bohemia and Moravia (separately!) would each become independent provinces with cultural autonomy.
You'd certainly see a separate Croatian province, with similar autonomy, incorporating the Croat-majority Southern part of Istria.
The Slovakians would get similar autonomy. Galicia-Lodomeria(-Bukovina) would be split into Little Poland (or whatever) and Galicia, although I could see the latter being sub-divided further, splitting off Sub-Carpathian Ruthenia to become its own province. In any case, each of these would also have cultural autonomy.
As far as the Romanian regions are concerned, a lot depend on how things play out with the Hungarians. I think the Banat, Southern Transylvania and the Romanian border strip in Bukovina will probably be organised as Romanian provinces. The Székely Land will almost certainly remain Hungarian, though, and Northern Transylvania (the region connecting Székely Land to Hungary proper) may also remain Hungarian -- or be organised as a culturally mixed region where Hungarian and Romanian both have cultural protection.
Trentino may remain integrally included in Tyrol (and thus Austria), but there's a slight chance that it might get autonomy, too.
Various German-majority regions may become exclaves, organised as part of Austria proper.
The Serbian-majority regions in the Voivodeship may well get autonomy, too. Since the POD is before the Austrian occupation of Bosnia, this actually opens avenues for the Austrians to become agents of Serbian independence.
For the moment, this arrangement would be stable enough. In the long term, there would be clear impulses towards separatism. Trentino for certain. The Serbs in the Voivodeship quite possibly (although, depending on circumstances, that might be allowed if it results in an Austrian-allied Serbia). The Poles will not move until there's a real shot at an independent Poland, but when there is, they'll want this (although, again, that could be a Poland under a Habsburg monarch, so the separatism might be formally endorsed as part of that scheme). The Romanians will probably seek to split off in due time, as well.
The Czechs and Slovaks aren't really in a good position for separatism. I think Slovenia may want more autonomy eventually, but will likewise stay within the Empire. Croatia, too. Sub-Carpathian Ruthenia and Galicia will have a bunch of Greek Catholics, so even if (Orthodox!) Ukraine ever gains independence, they may not have any desire to join that country.
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