Shoot 'em and put 'em out in the middle of a field somewhere for the vultures to eat, this way the vultures are fed and the bodies are cleaned up, even the mice and field rats will gnaw on the bones a little bit to get the calcium their bodies need (the small animals and others like foxes and coyotes and such will do this also, along with gnawing on dropped deer antlers to get calcium).
If it's done this way, the vet won't raise prices on *other* things (if they're euthanizing for free, there's no way they aren't upping the price elsewhere to make up for the time and money of the drugs used), and they won't have to worry about finding room to bury the carcasses or waste fuel and energy burning them.