How could we get the Italians to focus on colonization of Northern Africa over the Horn? An earlier Italo-Turkish War?
If the Franco-Russian alliance actually provides Ethiopia with assistance in modernization, you might see a stronger Ethiopia emerge under Emperor Menelik II and participate in the World War on the side of the Entente. Depending on how the World War goes and what its aftermath looks like, Ethiopia could embrace a unique version of Fascism that persuades it to ally with Fascist Italy and Imperial Japan which might be nothing more than a loose alliance.
19th Century Italy is probably too weak to wage a war with the Ottomans, or more pertinently to risk sparking the general war that such a blatant aggression would provoke (see OTL with the Balkan Wars.) Austria and/or Russia will jump in for part of the pie and London is likely to demand Italian withdrawal rather than risk Russia seizing the straits (at this point England is still generally pro Austrian and anti-French and anti-Russian in her outlook).
My read on it was basically Crispi (sort of like Giolitti, a proto-Mussolini of sorts) and the reactionary/conservative regime basically figured they'd embark on colonization to distract the unrest with some nationalist chest thumping (which backfired horribly when Ethiopia cleaned their clocks). So I guess avoid Crispi's regime, off Umberto a bit earlier (have the first assassination attempt succeed?) leading to internal strife opening a window of opportunity. Since France probably won't be allowed to take Eritrea and/or (more of) Somalia without a war/more concessions vis a vis Britain, that only leaves England herself or passing it off to a Sudan or Ethiopian protectorate as realistic overlords.
The problem is that Crispi was pretty fervently anti-French (which is sort of a prerequisite for an Italian focus on say Tunisia which itself is what's important here), and Conservative Italy is the Italy which was willing to reconcile with Austria- the liberals were all firmly pro-Entente/French and revanchist towards Austrian held Italia Irredenta in the Adriatic Littoral. On the other hand a worse socialist uprising or whatnot (or just a strongly pro-England/anti-French alliance) could be enough, especially tied to a worse Fashoda incident straining Anglo-French relations. Ethiopia taking Somaliland is a bit tricky, since England is more likely to "cede" it to Italy to stop France from claiming it... it's probably more likely to have England take it outright if the Italians aren't interested. On the other hand if Ethiopia is already an English protectorate they could quite probably claim Eritrea with London's backing. There's not really any major obstacle other than English approval, really, and the fact that Italy is substantially more useful to London than Ethiopia. Ethiopia probably won't have too much difficulty seizing the province since that whole region is sparsely populated (even today Eritrea has only 5 million people) and the fragmenting fringe of a faltering Ottoman Empire.
Another alternative is to somehow try and salvage the Spanish Savoy so they last longer than three years, if Italy is focused on propping up her cousins in Iberia she has plenty on her plate and will be very focused on curtailing the French and courting the British, the latter are also unlikely to allow Italy to expand into Eritrea if they also have "control" over Spain and are eyeing up Morocco, Libya etc.