Alright, in an attempt to start some discussion of this topic, and to finally do some form of TL, here goes:
March 1896: Battle of Adowa occurs as historically, except that this time the Ethiopians bag the entire Italian army of 14,000 men, half of the entire Italian force in East Africa at the time. The Ethiopians lose 20,000 soldiers, leaving them with 100,000 men for the invasion of Eritrea. While ammunition for their guns is low, captured Italian supplies give the Ethiopians enough for one more battle. Emperor Menelik, after considering his options, decides to go for the knockout blow. The Ethiopians begin marching towards the port of Assab, in southern Eritrea. Italian efforts to stop them are hampered by local resistance and the loss of the colonial governor (who was also the Italian general at Adowa). By the end of March, the surviving Italian troops are besieged in Assab.
April 1896: Despite the best efforts of the Regia Marina, the Italians in Assab are forced to surrender. With the elimination of the remaining Italian forces in Eritrea, Ethiopian troops spread out throughout the Italian colony, establishing their rule over the area. Ethiopian attempts in the world press to portray the Eritrean invasion as a consequence of Italian skullduggery in the Treaty of Wichale are generally successful; similar efforts with foreign diplomats are somewhat less so. At this point, however, Eritrea is a fait accompli, and the European powers have their own positions to consider. A speedy end to this rather embarrassing conflict is desired, and the Italians will simply have to accept it.
May-October 1896: Peace negotiations drag on for several months, ending only when the Ethiopians threaten to move into Italian Somaliland as well. In exchange for minor reparations and the return of Italian prisoners, Eritrea is ceded to the Ethiopians in perpetuity.
I'm not sure where this would go from here, but I do have a few speculations as to its effects on the European alliances. IMHO, both Austria and the Ottoman Empire would be quite pleased with an Ethiopian victory, perhaps to the extent of offering that country some form of monetary or technical support. I also think that France would, after some hesitation, weigh in on the side of Ethiopia. After all, that Djibouti-Dakar railroad they were after would of necessity have to go through Ethiopia, and a strong Ethiopia could be used as leverage against the British in Sudan. The French would also want to insure that they would be able to keep Djibouti. In the other corner, you would of course have Italy, along with Russia (opposition to Ottomans and Austria) and possibly Germany (opposition to France) and Britain (same).
Feel free to add C&C, along with your own ideas on where this could go!