When you call your local BA res number, do you know where the call is received during the normal business day? If in-country, perhaps you can call, manage to speak with a countryman with a little compassion, explain that you're booking the ticket ex-Mauritius and the sob's are having their problems getting you going, and meanwhile, would they mind booking the MRU-LHR segment for a fellow South African?
Lot of if's in there, but it's a free call and until you get a PNR they can't even keep score how many times they've told you to bugger off. Here in Los Angeles I'd eventually call one of the good folks on the AA rtw desk with the same request.
IBL immediately grabbed the space for me, btw. That may have been before the feeding frenzy on cheap ex-MRU began, though. (As ticketing is quite separate from reserving seats, I suppose you meant that you actually have the seats but are afraid the res will time out and you'll lose them. If that's not the case, BA/MRU is a sorry place to do business.)