What doomed Ian Smith's Rhodesia more than anything was a fact that the Rhodesian cabinet figured that they could win, led by van der Byl, who I might point out was probably the biggest, stupidest idiot in the history of colonial Africa. This guy ticked off and/or disgusted EVERYBODY, even Smith.
The best case scenario IMO is for 1980 to go as OTL, but in 1982 have Mugabe, Nkomo and Smith continue to work with each other. A large number of Rhodesians - something like half - had no intentions of leaving even with a black leader, and what drove them out was Gukurahindi and Mugabe's personal army, the Fifth Brigade. So, keep Mugabe and Nkomo from going their separate ways, and you keep Gukurahindi from going down, which in itself is massively helpful to Zimbabwe's economy.
van der Byl and the like would have ditched (as in OTL) but you'd find that the remaining whites would have played the game like Smith, Timothy Stamps and Roy Bennett did - competence over race. Not easy in Zimbabwe, but not impossible.
White rule? Impossible. It couldn't stand. If what they got in 1980 at Lancaster stood, that would have been about as good as it got. Best case for the whites is that the half of the Rhodesian whites stay (leaving Zimbabwe's white population by 1990 at about 130,000-140,000) and that Mugabe allows a handful of white seats to stay, say 5 or 6. Smith would occupy one probably until he died, and would have likely stayed the de facto leader of Zimbabwean whites. But what happened in 1980-81 was as good as it could have got. When Mugabe sacked Nkomo in 1982 and then accused him of plotting against him, then the crap began.
As for the theory of Mugabe have syphilis, keep in mind that several studies have proven that for many, syphilis attacks the mental functions first. Marius may well be correct in what happened.