Can price matches be done over the phone so that this can be discussed in advance? Or would that attract the offline booking fee?

At a travel firm I used to work for (tour operator, not airline) we always refunded pax in full if they didn't qualify for the price match even if it was their error, as long as it was outside of twelve weeks. This answers your questions re: can it be done and human interaction and so on - yes it can. But BA as a company have chosen not to when it's a customer error.