How long to cool off carcasses?

I know what you mean about legs sticking straight out. Last year I waited until after I finished all the birds I was processing, and there was a long-legged Rhode Island Red that I could not get into a bag. I finally had to have someone hold the legs down while I sealed the bag.

I now stick the carcass into a zipper bag immediately after I finish it, then bury the bag in ice to chill. I prefer to dry chill, and by bagging immediately the chick goes into rigor in the shape of the bag. The carcasses are chilled through within an hour this way.

 

The stiff legs are just rigor mortis. That goes away after a day or 2 in the fridge. I keep mine in ice water for a few hours then stick em in the fridge for 2 days. I cut up most of my birds, so fitting in bags is not an issue. For birds to be frozen whole I cut a slit in the skin over the cavity and tuck the legs. They still stiffen but the skin holds em back enough to fit in bags.