Why would BA (or any other airline) "give away" seats when they can get could money for them? Reward seats operate against the same yield controls as paid for seats. 2nd September is about the time people want to come home to the UK to get their kids back to school. The planes will be full with paying passengers.
As for MRU it's always full!
As Mariner 9 has said, if the airline is going to get some money, it's more likely to offer an upgrade but even then I'd have my doubts about early September back from Cyprus.