I have always used the rebar across the neck just behind the ears and then pull up on both hind legs cervical dislocation method of dispatching rabbits and have never had a failure. Then I hang them on a horizontally mounted piece of rebar from two twine loops around the legs below the hocks, and remove the head with a good sharp knife. I use the same bar and loops for butchering poultry too. As for the entrails, my dogs, ducks and chickens all gather around at butchering time and wait for those to be tossed to them and the dogs LOVE rabbit feet as chews. Since my dogs are fed raw food, as much as possible, I do NOT cook 'clean' domestic offal before I feed it to them, but I do freeze wild meat, which might be infected with parasites before they get that.
I put heads and hides into a fly factory, a plastic bucket with holes drilled into it and a tight top then hung where the ducks and chickens hang out, high enough so they can't get to the bucket. When the fly larvae get ready to pupate they crawl out of the holes and fall to the ground where the birds snatch them up. After a few months all that will be left is some composted fur, and bones if you also put road kill and other 'waste' meats/bones into the fly farm.
That way you get rid of the excess organic material and provide high protein feed for your poultry at the same time.
I do agree that most carcasses are best aged for at least a few days, either in cold salt water or dry before cutting. I age older poultry and venison for at least a week before eating or freezing. About the only carcasses we don't age are hogs, domestic OR (our much preferred over domestic) wild hogs, which we have in great abundance here in Texas.