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.