If you only spoke one or two agents then you should try to call them back perhaps different time, etc. some agents still willing to change the ticket whilst others won’t.
mid BA still refuses then you can take them to MCOL which will take about 8 months at least. So you need to buy a new ticket and claim that through the court. Kind of low effort but you have to make sure you keep the deadlines. If it’s a few hundred pounds maybe (big maybe) BA won’t defend it and could settle before the first hearing. So it’s up to you how you value your effort and time.