Did you open up the carcass so they could get to the insides or just toss the whole body? I open them up with a shovel or axe so they can get to the intestines and internal organs.
I do not leave the carcass in overnight either, same reason.
One time I was canning corn and had a yogurt cup full of corn ear worms. I dumped that cup out on the ground in a bare spot around a group of free ranging 10-week-olds. The chicks saw that pile. Slowly, step by step, inch by inch they crept closer and closer. A worm wiggled! Run away! Run away! But they did not run that far. Very soon, step by step, inch by inch, they crept closer and closer. A worm wiggled! Run away! Run away! But not that far. They repeated this 4 or 5 times before a brave cockerel got close enough to grab a worm. That's all it took, that pile was gone in less than a minute.
I don't know if yours will build up the courage and curiosity to check out that carcass. Mine generally do. I can get the same reactions to garden excess and wastes. Sometimes they immediately gobble it up. Sometimes they ignore it for a while but if one tries it most are soon eating it. Sometimes they just ignore it. The reactions can change from one year to the next.