A couple of months ago, I was planning three different weekend flights, all in discounted business, and on two OW carriers. Changing the dates for one trip (Non-BA), I confirmed the BA trip, not remembering the previous change, and at the same time I click Confirm, I see the wrong dates of the flights.

Since it was past midnight, I immediately wrote an e-mail to BA, explaining I made a mistake, and as the outbound (but not inbound) was non-flexible & non-refundable, and would it be possible to transfer flights one week later. I even offered to pay the same price, although the flights on the other weekend were 35+ £ cheaper.

Recieving nothing more than a confirmation of my mail beeing recieved, I called BA CS the next afternoon, the answering person had to confirm with supervisor, and change was accepted on the following grounds:
1. My e-mail was recieved less than 2 min after confirmation of reservation was made.
2. Beeing OW Emerald
3. Having a track record of correct reservations on BA
4. Travelling in CE
5. Asking nicely
6. On conditions I was aware of that this was a once-in-a-lifetime bennie
(7. Offering to pay the higher price, didn't officially weigh in, but was thought of as a friendly gesture)

Not exactly the same situation as the OP, but illustrating that if one confirms a non-refundable ticket, as per the airline, the deal is done. Politeness and some thin streaks of humbleness might sometimes work, at least once.