As I understand it, Italy offered to buy Veneto for a very large sum in early 1866. FJ turned the offer down, since buying and selling land would harm his Habsburg honour and sensibilities.
Well, but a short time later they agrred to give up Veneto anyway but without compensation. So that freed a least troops needed elsewhere? No, they still hat to stay there and put up a fight that was basically just for show. (And don't get me started on the reasons why which general was deployed where ...)
So I suggest this amendment of the PoD: FJ has a change of mind, listens to another minister, whatever. In secret, a deal is worked out with Italy - for five or so annual rates, Austria will give up a part of Veneto every year.
So, when the german situation rolls around, only a token force remains at the Italian border and the rest is available for Bohemia. Since military intelligence was not that developed, the Prussians overlook that and march into a unexpectedly superior foe.
The main difference would be that there are no uncompensated Austrian losses to Italy, so their need to take territory from Prussia is reduced. They leave Lower Silesia to Prussia and demand "just" the district of Oppeln and the five southernmost Kreise around Glatz - the area with a catholic majority (and, coincidentally, all of the coal and most of the industry).
The same time, the "Grand Duchy of Westphalia" would have almost the same population as Tuscany, to it goes to Ferdinand.
Trier and Koblenz (as the "Duchy of Trier") go to Franz.
The districts of Dusseldorf, A-la-C and Cologne become the "Grand Duchy of Julich-Berg" and go to the other Wittelsbach branch, the Gelnhausen line of the Dukes *in* Bavaria. They are close to the Habsburgs: Old Duke Max is the father-in-law of FJ, so either he or his son Carl-Theodor, Empress Elizabeths brother, will get the new crown, "returning Julich-Berg to the Wittelbach rulers".
Gibing Braunschweig to Hanover is also a neat idea, since the Braunschweig duke was unmarried and after his death, the Hanover line would inherit anyway. Perhaps Lauenburg, once Hanoverian and never part of Holsterin before 1815, is thrown in as well.
Interesting ideas. In particular, Italians and Austrians might negotiate all territories Italy has irredentist claims on. This might include buying Trentino but on the other side resettling Italians from Dalmatia and Istria into Italy proper. On the long run, an ethnically clear border with Italy should serve the Austrians well - although such a treaty not necessarily implies that Italy gives up all its irredentist claims.