I was waiting for an animal rights post. If you read my original post my preferred solution is to not kill them.
Go get a nice piece of land on a trout stream and have beavers tear it to pieces and we'll see how much you want to get a room with the beavers. Our swimming area now has a significant sediment build up because the dam slowed the current so much we are losing trees like crazy. Up river from the swimming area is flooded.
Oldken I like your solution. I just might be able to get a backhoe close enough.