I understand what you mean and it is often quite strange how unrealistic some peoples expectations are with regard to the everyday life and noises emanating from neighbours. Even well educated children make noise and of course have the right to do so playing and having fun.I guess I feel for the neighbor. My chickens are loud. All are hens. They're 75ft from the house and farther from my neighbors. In a 35 x 25 run. She still called the city complaining. Theres no noise ordinance where I live and I'm following all of the laws but man, I can't do anything else. Thankfully we will be moving to 26 acres so no neighbors but shes called the cops on my kids playing outside multiple times also. I'm not trying to be unreasonable but I paid for my house. I should be able to do what I want as long as its legal.
That being said, even having the right to do so and living on your own land it would always be kind to consider the neighbours. Some may work night shifts or have some medical issues causing them to be more sensitive to noise, whatever the origin.
The OP seems to have been very patient for three years which might in turn have led to some accumulated sleep deprivation and work issues as she seems to work from home. Of course it would have been better to address the situation much earlier, but maybe it is just now that the neighbours might have just added new chickens that are noisier than the ones they had before.
And this is exactly how I would try to start the conversation with the neighbours: Asking if they have added new chickens to their flock, as in all these three years before there was always some chicken noise, but never as loud and disturbing as it is now.