I can assure you that wouldn't work with me.  I would consider that a threat.  No need to ever ask me to look out for your house, when you are away, after a conversation like that.  I would do the deed as diplomatically as possible.  
"Excuse me, but I need to talk to you about a little problem I am experiencing.  (honesty)  I am missing too much sleep.  (obtain sympathy)  I have tried buffering the noise, (you have gone above and beyond) but I still hear crowing at all hours of the day and night.  (at this point be careful with your body language and facial expressions)  Can we discuss how to darken your chicken's surroundings during the night hours?  Or perhaps you can put all of them together and have a beauty contest with 5 contestants and the non-winners can be plucked and put in the freezer for later use.  (you are not only worrying about yourself, but also considering your neighbor's needs)  Only one rooster is needed for about 15 or more hens, depending on the breed.  (you are sharing a common interest)  Are you short on time or do you need more experience with slaughtering?  (concern again and the possibility of assistance)  I am sure that if we (you will help) can decrease the # of roosters in your coop, it will quiet things down for me and the other neighbors (you may not be the only one hearing the noise)and cost you less as well as improve fertility in your eggs, because if there are too many roosters, it is my experience that they fight instead of perform their intended purpose (professional)."
Or you can just find a 3rd party that is willing to help you by presenting themself as a person that likes his/her meat fresh and "Excuse me, but I was told that you had a few roosters and if you have more than you need, can I buy your extras?  I like to kill my own chicken, rather than buy them in the market."  You might even consider doing this yourself to be done with it.  Buy them or trade 2 hens for 4 roosters.  One rooster will still crow, but it has to be an improvement.  
If communication is good, you can work on the dark coop later on.  
The police should be avoided, if at all possible.  Call the police and you have an embarrassed neighbor that is mad at you and you might even have other neighbors making jokes about,"oh don't upset John; the police will come."  Now if you kindly go to him/her and do everything diplomatically and you get a flower pot thrown at your head and your life threatned and your dog is mysterously killed and hung from your oak tree in the front yard, then by all means, call the police.  I mean....we are chicken farmers; not trouble makers.