Could you not move the flights to a date that you could do? I don't have that much experience with reward flights to be honest (too disorganised to ever book in time) but of the onest I've taken I've missed two of them due to arriving to the airport too late (only 2 flights I've ever missed!) and both times I was easily able to move the ticket to a later flight at the airport with no cost to me (and one of those was a 2 leg flight with an AA flight on the second leg).

I do seem to remember trying to move one when in the cab to LHR (the whole M4 was shut down so I could see the writing on the wall) and being told I had to be at the airport to do it so maybe if you went to the airport on departure day and pleaded your case? Bit extreme perhaps and they may not be open to the "I just missed my flight - can I move it to one that leaves in 6 months time?" approach!