All right, let me take a crack at this:
Mid-late 18th century was a tough time over for Ethiopia, mainly because it was the
Zemene Mesafint or "Age or Princes/Judges" which was basically where the country was
de facto divided between the various well, princes with no real central authority except the divine right of kings. The one who put an end to it was Tewodros II over in the mid-to-late 19th century.
I don't seem to get much on how it happened so I don't know how to avoid it nor would I know which candidate would be best in doing so earlier so we have to work with what we have. Which would be with Tewodros II, who did alot in centralizing and modernizing Ethiopia of the time, though still hamstrung by some of the nobles and a few poor decisions. Namely, in trying to force the British to help him, which led to capturing people and the British Expedition to Abyssinia
, which didn't go too well for the Ethiopians.
Things really improved with Yohannes IV, which was late 19th century.
So you'd either need a strong king earleir to avert the
Zemene Mesafint for an earlier stronger point or for thhings to go better for Tewodros II.
The Expedition happened because he was trying to get help from the one of the Great Powers, and only France responded. Part of the reason was the letter having to be translated from Amharic. So, let's assume he manages to have someone in the court who could dictate his letter from assistance to make that easier. Who would respond? The French are out and so are the British, because they cared more on remaining in the good graces of the Ottomans. Interestingly enough, the letter to Queen Victoria was about Christian solidarity against the Muslim threat. This
might work with Prussia or Austria, though they were warring by 1866.
It's possible that if Ethiopia tried again with Prussia after Prussia's victory against Austria, I could see Prussia assisting Ethiopia in modernization and so on with military and the like, though that woudl require Willian or Bismarck to be okay with it. Granted, probably even some basic training there and the like would be a lot of help for the future rulers and help secure future assistance. Ethiopia could expand just as good if not better than OTL.
Interesingly enough, this could lead to further conflict as Ethiopia fights Italy with potential Prussian/German support and end Eritrea sooner, with Ethiopia becoming moe aggressive on asserting reign there. Another idea could be that Djibouti is lost to Germany or Ethiopia during the Franco-Prussian War there. Possible that Prussia/Germany would focus in East Africa and leave Djibouti in Ethiopian hands since it'd be easier though I would expect maybe German towns to be established there. Would further help with Ethiopia's development. I would think Djibouti might be supported in Ethiopian hands in the pretense of neutrality or whatnot, not in the hands of a European power.
Despite this, I don't think Ethiopia would formally join World War 1. While they could aim for the Suez Canal, being surrounded by the British would not make them entirely comfortable in trying. Guess it all depends on how far they advanced, though the British may recognize this and instead come up with a deal to ensure Ethiopian neurality. Maybe offer them British Somaliland? That would be a pretty good reason as it would expand their coastline.
I don't know if getting both British Sudan and Somaliland. Then again, the British were trying to stop Sudan from uniting with Egypy so depending on the situation, they might let Ethiopia take chunks of it and use historical precedence as justification. Ethiopia would probably be spending time consolidating its potential new holdings and developing itself. Also, aggressively reintroducing Christianity to the place. Also, one potentially screwy idea might be someone of the House of Solomon to take over German East Africa under the pretense of making it an official country, just so the Germans can spite the British and perhaps maintain some control there. I don't see it as likely given British occupation, but it is a possibility nonetheless. Hell, could go further and Germany release all their colonies to become Ethiopian vassals under the Solomonic dynasty, just to deny the British
.
Beyond that... kinda unsure. If things go as is, then we might see a Second italian-Ethiopian war though with Ethiopia beating Italy again and taking Italian Somaliland from them. This unties prett much the horn under Ethiopia. Beyond that, I don't see what more they could do besides consolidate their holdings and moderize though we might butterfly away WW2 or at least the rise of Nazism. Depends on German-Ethiopian relations and stuff on the economy and so on and if the above Germany spiting Britain by releasing their colonies to become independent countries, albeit under a monarchy of the House of Solomon would be feasible. I don't know how it would be enforcable outside of appreciation of enw management and possibly a strong military presence, especially through mercenaries. Then again, more than a few WW1 vets in need of work...
Hope you like this little thought experiment!