If the rooster is waking him up (which would drive me nuts too), keep him in a cat box within the coop, so he can't lift his head up to crow. My roo crows when there is a full moon from about 3am. So he gets to stay in the coop with his hen, but in the cat box now! I love my rooster, and I know if there are predators he will scare some off. My friend's two roosters died saving their hens from a fox attack. Roosters are AMAZING and UNDERRATED. My rooster finds special treats for his hens and stands guard while they eat.
Good luck with him, he is beautiful.