PP ....
I don't know anything about this kind of thing, but I have a hunch you are right about a wild hawk targeting live prey. I see the hawks flying over the meadow below as they hunt for food every day. I've never actually seen them going for road kill. I think they leave that for the ravens and crows ...
I think your idea of a chicken or smaller prey may be more on target than a hunk of meat because you are dealing with a bird that has never survived in captivity and probably does not recognize even a warmed hunk of meat as food. Do birds have a sense of smell ? I honestly don't know ..
I am unsure about having the chicken in a cage would work for you. Of course, I've never tried to solve this kind of problem, so what do I know ?
Just a thought and yes, I know it seems inhumane ... is there anyway you can tether the prey to a post pounded into the floor of the barn near the door of the barn ? The chicken will will then move around and squawk in fear, which may bring the hawk down and if it's near the door it may go for the prey or it may go out to freedom.
Chickens on farms are not pets, so if you have to sacrifice one to save the hawk, you may not think of the chicken the way we do where we are not commonly raising chickens.
Smiles,
Lyn