I’m glad you got sorted. The history of this IIRC is that the policy used to be more flexible. BA tightened it up in the aftermath of Covid, presumably because of a fear that travellers were using all the flux in the schedule to book cheaper itineraries and then switch them for more expensive ones when the schedule changed. This led to the current policy. I think many agents heard the part about ‘affected segment only’ without hearing some of the caveats.

In my view the current policy is somewhat too rigid, for example if a passenger has a change that pushes them forward by a day on the outbound, they can’t push their inbound forward by a day to maintain their trip length.

It should also be said that the online tool doesn’t 100% stick to these rules. So for simple itineraries worth checking what it will offer.