The "bigger history of strong centralized empires" and talk of the failed attempts to subdue it before made me think of the tantalizing longshot: It becoming a "Southern Ethiopia" which can uparm and successfully resist the Europeans.
The people who know more about it than I could undoubtedly poke a million holes in that claim, but I can still imagine (esp. for a soft story) the right combination of skill and luck enabling lightning to strike.
Honestly, Colin, I don't think this is that unreasonable.
Like the short version of 'why ethiopia?' is they were included in the area of an influence of a weak European power who botched the diplomacy by arming then, then botched a war and then gave up.
If we sketch out a timeline. Rhodes is off the table for whatever reason, he doesn't come to Africa, he doesn't become rich. Nobody then offers to fund British advancement in that area, which without Rhodes they wouldn't. So when Germany recognises Portuguese control over Zimbabwe and Zambia in the mid 1880s, Britain follows up with their own recognition.
Portugal then makes a deal with Lobengula, who wants to make a deal hence why he made one with Rhodes, as part of that Portugal start selling him weapons or allowing weapons to be sold through their claimed land which they often did in that area.
So now on all the maps the Matabele are coloured in Portuguese but they don't consider themselves conquered. Eventually there is a centralising kick in Lisbon, someone attacks the Matabele and the portuguese lose like the british did at Islandlawana. Only the portuguese, always operating on a shoe string compared to the other colonisers, don't have the man power to recover and agree peace.
Zimbabwe is then recognised as independent.
I don't think that's super likely, like you say it involves the Matabele rolling sixes, but I can buy that, especially as a soft AH story.
There is of course the argument that a pagan zulu style militarised society ruling over foreign peasantry is far less stable and likely to be accepted by Europe than a centralised Christian state. And that's possibly true, though I think the affect of Ethiopia's Christianity is somewhat over stated. Luckily it's quite easy to get a christian shona state.
Mwenemutapa Negomo Chirisamhuru of the Kingdom of Mutapa coverted to christianity in 1561 as part of a proxy war between muslim arabs and catholic merchants. He however then renounced that under pressure form the muslims later in 1561 which led to the 'Accidental Crusade' of 1568 and the Mutapa defeating the portuguese then. A few changes there, Mutapa emerges as a christian Portuguese ally and then the murder of a bunch of butterflies and we're back at scenario one.