I hunt with just an ice chest and a camper shell as far as creature comforts. That makes it hard to keep birds for very long when the night time temps are above freezing. When below, I just put the birds on the roof of the shell at night and back in the ice chest during the day.
Has anyone tried to dedicate a small ice chest to an ice brine cooling system where you'd keep the cleaned birds in a smaller water tight container buried in the brine? A 20% salt brine results in a 2 deg F. temp for the brine. It would require going through a lot of ice and salt but that's better than having to leave soon after getting birds to prevent spoilage.