I have reread the TL, and apart from heaps of praise, I do not much to acomment about, in addition to express my agreement about LK's suggestions. About the peace deal after the I-G-F war, I heartily suggest the following: Germany and Italy ought to get more or less comparable territorial gains from the peace deal. This might mean the satisfaction of basic respective irredentist claims (OTL Alsace-Lorraine and Luxemburg for Germany, Nice, Savoy, and Corsica for Italy) or we may have the victors get a bit more greedy and push for a bit more questionable but valuable claims. Given that this is a (well-done, plausible) wank, I suggest the latter. For Italy this may mean getting eastern Algeria and the French Riviera up to Toulon. Given that diCastagna is a business-minded statesman, who has invested in tourism, he can see the economic benefits of getting the Riviera ("Italy, the tourism center of Europe, sporting all the best seasides from Toulon to Ragusa"). Additionally, he might also grab a slice of Alpine territory between Savoy and the Riveria to ensure that Italy fully controls the watershed throughout the Alps. In turn, Germany ought to get all of the Alsace and Lorraine provinces, and move its border with France on the Maas/Meuse. More territorial gains than this are IMO excessive in 1869. The Italo-German Axis can always get more when they curbstomp revanchist France in the next war. I think that giving all French shares of the Suez canal to Italy may be a little excessive, but certainly Germany and Italy can split the French shares in equal parts between themselves like good partners.
Because there shall be a rabid revanchist and nasty France. ITTL there shall be an even bigger Commune that sweeps Lyon and Marseilles as well as Paris (aftereffects of the Italians besieging the former two cities). The reaction to this, in addition to Papal presence in France, and the Second Western Schism that Pius' actions unleash (full support for LK's ideas), shall lead to a Bourbon takeover in France soon after the war. Some ambitious French general shall become the strongman and real power behind the throne, and use both revanchist feelings from the war, middle-class revulsion to Commune excesses, and ultra-Catholic mobilization to build a reactionary-protofascist regime. Think of an early successful Boulanger. The regime shall be one half the reborn Inquisition, one half French proto-fascism. Ultra-Catholic mobilitation shall buffer up Carlism in Spain, and the Carlist pretendent to the throne of Spain is, conveniently enough, next into line for the Bourbon throne of France after the current pretendent, the Count of Chambord. Therefore, France supports a Carlist takeover in Spain and creates a dynastic French-Spanish union.
The Pope sets up shop in Avignon again (the place has tradition and a kickass Papal palace), and gives ideological support to France-Spain and the Bourbon-Carlist regime as the "sword and shield of the true Church". In turn, Bismarck and di Castagna give full support to the Old Catholic church and denouce the Pope as the obscurantist puppet of the French. Soon the OC, tapping into nationalist German and Italian anti-French feeling and liberal middle-class opinion, get the allegiance of German and Italian Catholics. Their Church becomes a powerful agent of social and political modernization for both Germany and Italy (and their satellites, like Hungary), since it becomes a quasi-Anglican progressist organization strongly involved into social issues, which gives an handy quasi-Fabian alternative to marxist socialism for the mobilitation fo the lower classes and prevents the political alienation of Catholic voters. This in turn reinforces the sympathies of Britain and America for the Italo-German bloc, seen as the European champion of liberalism against Bourbon-Tsarist obscurantism. More British investments for Germany and Italy, and ideological underpinnings for a powerful Triple Alliance.
The Habsburg Empire's downfall and the Russo-Turkish War unfold pretty much as LK and other posters have suggested. At the Congress table in the Hague or Bruxelles, a compromise is reached about the new settlement of Europe. Italy gets a protectorate over Montenegro, Tunisia, Tripolitania, and Cyrenaica, as well as the administration of Crete. Germany annexes Austria and Bohemia-Moravia. Slovenia may become an independent Italo-German satellite, or be partitioned between Italy and Germany, your choice. Bosnia becomes an independent principality (Italian satellite) under a Savoy-Aosta King. Hungary becomes an independent kingdom (German satellite) under an Hohenzollern-Sigmaringen king, with Slovakia, Croatia, Transylvania, and Banat. Serbia and Romania become independent. Bulgaria (in modern borders, with Eastern Rumelia but no Macedonia) becomes an autonomous principate under nominal Ottoman overlordship. Greece gains Thessaly and southern Epirus. Britain gets administration of Cyprus. The Ottomans keep Albania, Greek and Vardar Macedonia, most of Kosovo (a northern slice goes to Serbia), northern Epirus, and Thrace. Russia gets southern Bessarabia and its OTL gains in the Caucasus. France gets the powers' acceptance of its dynastic union and close political ties with Spain.
Britain is pleased with the support that Italy and Germany gave to its positions, and gets closer to both powers. Russia is annoyed for the same reasons, and gets closer to France-Spain. You may see the seeds of rival alliance blocs, and an ideological proto-Cold War, between reactionary-revanchist France-Spain-Russia, and moderate liberal-nationalist Britain-Germany-Italy-Hungary(-Ottomans). Althtough the latter have a lot of modernization to do, and are not regarded as a real great power at the moment, and Hungary ranks as Spain, a medium power that is the useful sidekick to a great. In the coming three decades, British investments make Greater Germany even more of an outstanding success story than OTL, and let Italy accelerate its pace of industrialization and economic development to levels only reached by 1950s-1960s IOTL. German and Italian economies become very integrated as in late OTL 20th century, as well as sporting very similar political systems, steadily getting similar to the British one.