The first one was rerouted by the Qantas in-town ticket office in HKG (I went and did something else, but it was ready within 90 mins), and then rerouted again by CX at HKG airport (done within 25 mins).

The second ticket was rerouted by the BA ticket desk at LHR T4 flight connections centre. This took longer - essentially because the people there didn't have a clue about this type of ticket. But I was sitting inthe Concorde Room sipping champagne while they sorted it out, so it was no great hassle to me, except that they charged me 25GBP "ticketing fee" in addition to the normal USD75 reissue fee.