I'm sure this has been resolved by now but I had to tell you that we once had to smash a kitty with a boulder under very similar circumstances...
kitty was so young too, it was heartbreaking but ultimately it was either that or let the poor thing suffer.
I'm late on this one but the bunny breeders I know will put a lost cause rabbit in the freezer. They just drift to sleep from the cold. I'm glad it's not a lost cause though