My recent attempts in new bookings or change booking have seen the waiting time from 3 hours (Change booking) to 48 hours (New booking).
Check every few hours on MMB to make sure the proposed new segments stay in Confirmed status - if it is labelled as CANCELLED, call BA immediately to get it stick into the PNR again.

In my recent booking where back office is involved, QR segments seems to stick well in the PNR throughout. Given your change is on different date and different route, the risk of getting auto cancelled for duplicate/impossible itinerary should be minimal.