This is very well done, and very well researched, but I do have a few questions, and a few things I find implausible.
1) The Rhodesians supporting the Portuguese and then RENAMO is going to make very, very unpopular in Western Capitals, and it may well cause the Soviets to give more guns to ZIPRA and ZANLA, or worse make either of those two groups accept help from Cuba. Castro's troops in Angola forced the SADF to get into the act and virtually wrecked the country. If the Cubans show up, so will the South Africans, regardless of what Salisbury thinks about it, and that'll be doubly true as Cuban communists in Angola can't really harm South Africa itself. Cuban forces in Rhodesia definitely can - from there, they could bomb Pretoria.
2) RENAMO NEVER had the ability to overthrow the government of Mozambique, and I highly doubt Salisbury's forces could completely change that. They were primarily used by Pretoria to make sure South Africa's neighbors could only move goods to the outside world through them. (They supported UNITA for this reason, too.) If you are desperate to keep the Beira corridor open, you'd be better advised to have Salisbury do that job themselves, or pay off FRELIMO to look the other way. (Given enough money, FRELIMO probably wouldn't have too much difficulty allowing Rhodesian naval units and/or transport corridors.
3) The Rhodesian Air Force attacking a Russian naval group is asking for a major response, and Soviet SAMs are pretty good. I don't think the RhAF could strike at that group, especially considering the fact that their air force would be a worn-out, crumbling mess by 1984. Against a Russian carrier group, even with having lost their planes (Which is easy - Yak-38s suck. A Hunter with a good pilot could blast it with little difficulty) would still easily shoot down any RhAF aircraft attempting to attack them. I can't see many options for new aircraft open to them - the South Africans will need everything they have for the Cubans in Angola, nobody in the West would consider selling to Rhodesia, the Communist bloc won't for all the obvious reasons. Israel, maybe, and perhaps the Rhodesians buy Canberras and Hunters from some places not using them (Peru, Chile, Lebanon, Saudi Arabia). The Israelis would be the only option open to them for new planes, unless you can get Taiwan advanced forward to the point where the Rhodesians could buy the Taiwanese indigenous fighter.
4) Does this Rhodesian Armed Forces have the ability to make more sophisticated gear? You've mentioned ammunition plants and Rhodesia had plenty of ability to make raw materials, but sophisticated stuff would be more of a problem, particularly with regards to missiles and more sophisticated weapons. Having guys like Gerald Bull around helps with this, but Rhodesia still does not have the economic strength or technical sophistication to do much of what it would need to be totally independent. South Africa does, but as you rightly point out, the apartheid state had little love for Salisbury.
5) Even with many more educated, employed black Africans, how does the economy take all of this? Rhodesia's Bush War racked up a half-billion-dollar debt between 1965 and 1980, a big sum for a nation of seven million people. Unless you can (substantially) increase the white population, you won't be able to get the economic strength to handle all of this.
6) The chances of Major recognizing its existence border between zero and nada. Heck, I'd say its even less likely in the 1990s, with apartheid crumbling and the Cold War over, why recognize this mostly-insignificant place which will soon be the only place in Africa to not have gotten its independence through free elections? Major never held the strongest of political hands, and the Commonwealth, particularly Canada, India and Australia, would be very pissed about Whitehall giving Rhodesia official recognition, especially after all three ripped Pretoria over apartheid so many times. If you want to get recognition, you're best bet is to have Thatcher do it in late 1982 or early 1983, after kicking the asses of the Argentines and having the ability to claim its recognition of Rhodesia is meant as a contain-communism move. Thatcher had a good political hand at that point, too, as the Michael Foot era Labour Party couldn't find an electable position with both hands and a map.
For all my minor beefs, I still commend you sir for a well thought-out, well written TL.