Insulate the cages from ground and wire them up to 240 Volts or 480 Volts with appropriate warning signs and disconnect switch where they can't get to it. I'll bet they won't touch it more than once. They'll pick an easier mark next time(if they survive). Maybe just having it LOOK LIKE it's electrified may work with some. Although I have heard of some people stealing ground wires off powerline poles, till they got hold of one that was energized, that's usually where their copper theft career ends, permanently. Can anyone say Crispy Critters?
An electric fence charger may be all that's needed to deter most theives.