I wouldn't worry unless it's taking your over an hour. Ideally, they should be cleaned and cooled to under 45 degrees in less than an hour, but there's some grace period. Remember, sometimes hunters don't get to gut their deer until the next morning, and the meat is fine, depending on temps. Butcher one bird at a time, go as fast as you can (doing it safely and correctly,) and keep ICE COLD water on hand to get them cold as soon as possible when you're done.