I posted this question a couple years ago, but since the thread doesn't seem to die I'll give another update:
whatever weapon you're using, the best way to avoid meat damage on rabbits is to just shoot them in the head.
-Since first posting, I've gotten much better with a shotgun. In open country, it's usually pretty easy to get a head shot. They never seem to run straight away, so it's just a matter of swinging a little further in front.
-I've been running into snowshoes on spring bear hunts and harvested three with a 308. A headshot looks pretty ugly, but doesn't damage the meat at all.
-I've also been doing a ton of damage control rabbits. Here in Oregon, they're legal to take from the truck with a pellet rifle. On these, I just aim for the eye and they flop right over. It's nice because pellet rifles don't have the power to knock them down otherwise.
-I also get a lot of trapped rabbits. Those I grab by the hind legs and whack the back of their heads with my fist. Those are the best!