1) It depends very much on the individual agent you get. I have had good experience at the ticket desk in T4, but bad at the transit desk there. Remember also that reissuing with BA will cost you GBP25 more than reissuing with CX. I assume that you are taking CX F LHR-HKG (if not then why not? it is much better than BA) so why not get CX to do the reticketing? I have no experience of them doing it at LHR, but everywhere else I have used them they have been fine.
2) No reissue is ever totally painless - the problem always being taxes and surcharges. To be honest I doubt that the extra paid segments would be any worse than changing to two different SWP segments, provided that the agent doing it is familiar with the rules on extra paid segments. In any case allow at least 90 minutes EXTRA to do the reissue if you plan to do it before your next flight (so if I was taking CX ex-LHR I would be at the ticket desk 3 hours before my flight).

Hope that helps.