Hi FTers,
Got a couple of updates - and an apology!
So finally my family arrived in Mauritius!! I followed the advice above and got to the airport early (

), and watched my wife's and daughters' flight arrive - rarely have I been so happy to see an aircraft land (and I say that as a licensed pilot of 30+ years)! Saw them walk from the aircraft to immigration (separated by glass!) - finally they were amongst the very first to exit arrivals - the joys of HBO!
As BA2065 was descending into MRU, I went to the Air Mauritius check-in desk, explained the situation (MK flight on Saturday MRU-JNB with Chinese passport, no SA visa wife connecting to LHR later same day on BA), and sought confirmation that she would be allowed to board. "Yes of course", with an animated delivery. I spoke to the check in agent (soon joined by another) for 3-4 minutes; she explained emphatically, with those delightfully French-inspired facial expressions and hand gestures, in multiple formulations, that this was 100% OK. They wondered why I wondered - I (briefly!) explained the saga at LHR - and they reacted with incredulity.
All's well that ends well? Not really, Wife was fuming at BA when she arrived. She has enjoyed a relaxing day of holiday in a delightful place, but she is in the mood for recompense.
Lastly (for now) an apology. I said I would do a slew of replies to people's messages last night, but I was so tired after sleeping 3h the night before, I slept! But people have made lots of interesting points, and asked relevant questions, since I last replied in detail, so I certainly will in the coming few days.
So thanks again all! Saga is now "stabilised, but not concluded". Will, as always, report back in an open and transparent way, to ensure others can learn from this episode to the fullest extent possible.
BTP