Not a lot of options really. Other than purchasing some kind of ground arrangement (hotel, experience, etc) through BA, you might as well purchase something cheap on AS/AA and do a mileage run, especially if it won't cost you anything but time.
If you really, really want to give the money to BA, you could maybe buy a shorthaul something that ties in with your March trip, or put it towards a fully flex shorthaul that you can then use towards a future booking - but USD280.00 will only go so far towards that; the lowest I could find looking quickly was a fully flex LHR-LBA oneway at USD351.70, meaning you'd have to pay an extra USD72.00 out of pocket. Not really recommended as when you come to apply it to a future booking, you'd have to do it over the phone and may be limited on what you could apply it to. You'd still be able to get a refund less a processing fee if you couldn't use it in the end...