When we butcher as soon as we get done gutting and cleaning them. They go in a cooler full of ice and salt. These are usually a 10 to 12 week old broiler or cx's meat bird. I don't know if this is what you are calling "brine" but it is what we do.
After they soak a bit we piece them out or put them whole in freezer bags and they go in the freezer or we take them to get smoked. When we take them to get smoked we leave them in a cooler with bags of ice to keep them chilled.
You are chilling them after you kill them right?
I hope this helps.
Nick