MacCaulay, if you need help on sub-Saharan Africa at the end of colonialization, look to me and Marius, friend. My father and grandfather lived it.
Now, getting Rhodesia involved in the Congolese civil war isn't terribly hard, as the Congo was a mess and the first independent leaders felt that the UN had a responsibility to help destroy the independence movements in Katanga and Kasai provinces. Attempts by the UN to gain control went south immediately, and the Belgians stayed around causing a ruckus.
You'd have to keep Rhodesia as one nation, which is not easy to do in the 1960s. Better idea is to start in the 1950s, and advance the liberalization of the Federation of Rhodesia and Nyasaland, and thus bringing the likes of Robert Mugabe, Dr. Joshua Nkomo and Kenneth Kaunda into the government. Problem there is a potential split in the country - don't bet on Ian Smith taking the idea of black rule too well.