Cock a Doodle Don't

We're in need of some family planning on our farm.  We don't cull anybody and we don't eat anybody either so if all is left to one's own natural instincts, we get more chickens than we can handle.  The cacophony at the moment around 5am is concerning.  Every rooster trying to out crow the other leaves us wide awake wondering why the most popular spot appears to be under our bedroom window.  I've been attempting to cease the broody hen situation by turfing Patsy out of the nesting box on a daily basis.  Apart from the fact it must be at least 45 degrees in there (it's tin and only insulated with spider webs), every afternoon I pick her up and toss her into the chook yard to eat and drink.  Which she does and then returns the next day.  And more often than not there is not a single egg under her.  I'm at a loss as to why she'd persist with this.  Hens being on some occasions more smarter than we think, then hide a pile of eggs under a tree or shrub somewhere only to emerge about 4 weeks later with a fluffy dozen like the ones in this picture.  And as cute as they are, when they start to crow, not so cute.  The learning to crow stage is pretty funny though.  Some will get up to pitch but fail to hold key.  We've got one out there at the moment that sounds like someone has pulled the plug on him half way.  A bit like the sound of a record player being turned off at the power mid way through the tune (if you recall such a thing).  So the next person that talks about the peaceful life of country living, I will understand - has never actually lived there.