I have an FAC Rapid 7 and it's good for rabbits out to 60 - 70 yds, trouble is I'm not quite good enough (yet) to use it's capability. Would go with the previous thoughts on going for a rimfire etc, but if that is not a prospect that suits you, consider a S16, Logun Axor or Rapid 7. I might be temted to shy away from the AA 410, as the overall length starts to get a bit too long.
Dan