Yeah, thats probably the main problem this TL would have to overcome.
Any way to make Austria experience a revolution after 1866? Say, they help France in the Franco-Prussian war, and subsequently get invaded by Prussia/Germany, which hands several major defeats to the Austrians. This prompts uprisings across the empire-Hungary declares independence and Polish nationalists take power in Galicia. In Vienna, radicals take to the streets and proclaim a "Republic of Germany" as the Hapsburgs flee the city, and Bohemia experiences running battles between Czechs and Germans. Bismark responds to this disorder the only way he can think of-pressing the invasion and occupying German Austria and Bohemia. Meanwhile, Russia invades Galicia and snuffs out the Polish nationalists before "their" Poles get ideas, and the two cooperate in insuring that Hungary comes under the control of its safely conservative aristocracy.
In the end, the incipient revolution in Central Europe has been defeated, but all notions of an Austrian state have likewise gone out the window. Bohemia and German Austria are absorbed into the German Empire, Hungary gets Hohenzollern prince as its new king, and Russia gets Galicia for their trouble.
Remotely plausible?
This is very plausible, especially if you expand the 1870 war to a general European conflict of Prussia/Germany, Italy, and Russia vs. France and Austria. For best feasibility, this lineup requires a somewhat better Italian performance in 1866. It skirts the limits of the OP, but not really breaches them, since the main effects of the PoD are all felt later, apart from somewhat better Italian territorial gains at the peace table, such as surely Trentino and quite possibly either Gorizia-Gradisca or Dalmatia as well. Admittedly, this is not strictly necessary, in all likelihood Italy would be strongly motivated to side with Prussia/Germany (and Russia) even with OTL 1866 performance if France and Austria ally, but the scenario works best this way.
Moreover, the victory of the anti-Prussian revanchist faction in the A-H ruling elite is necessary: Hungarian Premier Andrassy, which was a strong neutralist, needs to be removed somehow so that Austrian Chancellor Beust, a staunch revanchist, can have his way. Again, a slightly better Italo-Prussian performance in 1866 also feeds this second PoD, nothing so radical as to cause the rapid collapse of the Habsburg state in 1866-69 (the success of the Ausgleich, however shaky, is essential in this regard), but enough to make Austria more resentful and paranoid than OTL. Austria is going to overestimate French military prowess in 1870 as outrageously as France itself, and expect a quick and easy revenge war with the Austro-French alliance.
Unknown to Vienna and Paris, Bismarck had secured a secret counterinsurance agreement with Russia in 1868 and 1870 which guaranteed a Russian intervention in Galicia if Austria joined France. TTL Italy publicly sticks to alliance with Prussia, which makes the Hohenzollern and Savoia candidates to the Spanish throne equally unacceptable to France and just as likely that France shall overreact and escalate to war in the Spanish Succession crisis, even more so with Austria in its pocket. This of course assumes that Prussia and Italy, made bolder by greater success in 1866, do not simply choose to stand their ground in 1867 over the Luxemburg and Rome crises and provoke France to war then and there, when Austria would still be deep in the aftershock of a worse 1866 war and mired in the throes of the Ausgleich crisis, utterly unable to join the war. But for familiarity and simplicity we may assume that Bismarck (and the Italian government in tow) avoids war until he has secured the support of Russia and the southern German states. This is all but guaranteed if France and Austria are noticeably growing closer.
So France declares war to Prussia and Italy over some trilateral equivalent of the Ems Telegram, Austria joins France, Russia joins Prussia-Italy, so do southern German states out of both treaty obligations and an overwhelming grassroots wave of German patriotism. Britain stays neutral since they don't really fancy French expansionist claims in the Low Countries which Bismarck cleverly leaked to British press. Germany and Italy take a defensive stance in the West for a while and join hands with Russia in a three-front offensive against A-H. Austrian military situation soon turns from bad to worse, Austrian German and Magyar nationalists, never really enthused with this war to begin with, read the writing on the wall and rise up, nationalist clashes occur in Bohemia-Moravia between Czechs & Germans and in Istria-Dalmatia between Croats & Italians, quickly won by the latter side when advancing Italo-German troops quell the Slavic nationalist opposition.
The Hungarian secession seals the military and political collapse of the Habsburg state which is occupied by the alliance. German-Italian-Hungarian cooperation also snuffs out any attempt for Croat independence, since Germany and Italy favor the continuation of the Hungarian-Croat union to quell Slavic nationalism. Germany and Italy transfer the bulk of their forces to the Western front and overwhelm France like OTL, only more so as Italian forces exploit German victories to make a strategic breakthrough of their own in the Rhone Valley. France kicks out Napoleon III, makes a stubborn but futile attempt to reenact 1793 for a few months but is eventually forced to surrender by hopeless military situation. Cue Commune strife in Paris, Lyon, and Marseilles, and a postwar France even more revanchist and politically instable than OTL, except they now prefer to eat German innards for breakfast seasoned with Italian blood.
Overwhelming pressure from German nationalists, insistence from the Italian ally, evidence of repeated Habsburg hostility, and reality of Hungarian secession combine to make Grossdeutchsland a clear necessity even in the eyes of Bismarck and the Junkers.
At the peace conference Germany annexes Alsace-Lorraine, Luxemburg (bought from the Dutch King with part of French reparations), Austria proper, Bohemia-Moravia, Slovenia, and South Tyrol, Italy gets Nice, Savoy, Corsica, Trentino, Kustenland, Dalmatia, eastern Algeria, and Tunisia, Russia takes Galicia and Bukovina. Germany and Italy also seize and share ownership of the French shares of the Suez Canal (half of which they decide to sell Britain and win its benevolence, an agreement the three powers later replicate with the Egyptian shares when that country suffers financial collapse) and of French Indochina. Franz Joseph abdicates and some members of the Habsburg family which are willing to cooperate with the new order get the thrones of Austria and of Bohemia-Moravia as member states of the German Empire. The victors and the Magyar magnates pick some member of the German royal families as the new king of Hungary, which keeps Slovakia, Transylvania, Vojvodina, and a federal union with Croatia-Slavonia.
Given the nominal casus belli, one would naturally expect a Hohenzollern or a Savoia (toss a coin) king on the throne of Spain, but it is also actually quite possible that Berlin and Rome graciously accept to restore Alfonso XII as a balance of power concession to Britain. Or sheer Spanish political instability just causes the Bourbon restoration a few years later with Berlin and Rome not bothering enough to intervene and enforce the status quo.
The CP bloc of Germany, Italy, and Hungary establish a free trade pact and a military alliance which is much more stable and cohesive than OTL, masterminded by Bismarck. His main strategic concern becomes to balance the CP bloc between Britain and Russia, in order to keep both powers reasonably content and France isolated, Russian influence in the Balkans and the Middle East within sensible bounds, and German-Italian successful colonial and commercial expansion not seriously antagonized by Britain. With Austria out of the picture, the CP bloc stronger and stabler, and the European balance of power simplified back to five main players, this balancing act becomes easier and in all likelihood more successful than OTL, which ensures larger German and Italian colonial empires, shrunken French and Portoguese ones, and no Belgian Congo.
Bismarck the founding father that unified Grossdeutchsland (despite his previous misgivings, he's later going to claim he planned every step of the path to it beforehand) is unlikely to be ever dismissed, and stays in office pretty much until his death, which ensures a clever CP diplomacy to continue the balancing act, and no blue-water Italo-German naval craze to antagonize Britain, till the turn of the century. After his death, all bets are off as it concerns the places of Britain and Russia in the European alliance system and the occurrence of *WWI, although in all likelihood the CP are going to come on top of it nonetheless, and make this 20th century a CP and American one first and foremost.
In comparison, the outcome of the British, Russian, and Ottoman Empires largely depends on whether the World Wars occur and which side they pick or are pushed into (although Ottoman rule over Christian Balkan nationalities is a wizened relic of a bygone age which is not really going to stand), it may be much better, not really different, or much worse than OTL. In all likelihood, France lets revanchism drive it into a worse and worse mess, quite possibly akin to OTL Germany (although with much less destructive consequences for Europe at large). It is too late for this PoD to affect Japanese modernization significantly, although strategic and diplomatic butterflies may well drive a wholly different outcome to the Russo-Japanese clash, which may cause a worse short-term, but an happier long-term outcome. America is going to keep blazing its quiet path to top-class greatness, although it shall have to share the superpower league with the CP bloc at least, Britain and/or Russia optional. It is anyone's guess whether butterflies may ensure a successful Chinese modernization in the late 19th centiry. If they do, China may expect a much happier course in the coming century, if not, a very "interesting" period as usual, except there are going to be more Germans and Italians, and less French, around to exploit it.