Neighbors have a VERY LOUD rooster. Any advice?

I live in Houston (outside of the city limits, but I'm within Harris County and my address is XY street, Houston, TX). I've been in my house for over 9 years, it's a typical nice suburban neighborhood with small/medium sized backyards and an HOA. The neighborhood has always been fairly quiet and my next-door neighbors have been great over the years.

One neighbor I haven't talked to before (never see them) decided to get a few chickens at the beginning of the pandemic. The chickens have always been at acceptable levels of noise and never bothered me, and my toddler and I could look at the chickens through the fence. They're pretty cute honestly- they occasionally cluck but it's not loud or something to be bothered by at all. I knew it was against HOA restrictions but I don't care, they weren't bothering anyone. I hoped they were enjoying their home grown eggs.

Well they bought a rooster 2 months ago, I'm not sure why exactly since their small chicken setup seemed great for over a year. Their backyard is on the smaller side and only about ~40 ft from my bedroom window. The rooster starts crowing around 4-6 am every day (before the sun is up) and goes all throughout the day until dusk, legitimately 200 times a day. Sometimes it crows every 10 seconds for several minutes. I live in a row of about 20 houses with backyards all facing eachother so the sound echos through the canyon of homes.

It's loud. I've hung up thick curtains and bought a white noise machine and multiple fans, but it's still faintly audible even then. My child's room is in the front of the house away from the rooster and he can still hear it. It wakes us up almost every. day. We're sleep deprived and my kid cries now in the mornings because the rooster won't shut up. On rare day it doesn't wake us up it's annoying throughout the day to constantly hear it. My husband's been working on an important project with his coworkers this past week and was struggling because we're not getting enough sleep, and his coworkers can even hear the rooster on his Teams calls (he's WFH).

I love the idea of having gardens and chicken eggs in urban environments for food production, but the rooster noise is driving my family nuts. It doesn't even sound well, I'm actually worried for the animals due to the small space and how many they have now. I've seen the rooster in the chicken coop during the middle of the day, it seems distressed.

I tried talking to the neighbor to see if we could work out something to dampen the noise, anything, but he just told me to wear earplugs and closed the door angrily. I've tried. I can still hear it and earplugs make my tinnitus worse. The neighbor heads to sleep super early (I can see their lights turn off) and wakes up to feed the chickens at 6 am (I hear him in the backyard and the chickens going crazy for food) and then goes to work so it doesn't seem like he's bothered by the rooster since it's never really crowing when he's asleep, and he's gone all day and doesn't have to hear it. My family and I are all here during the work week, so we have to hear it all the time.

I hoped they would get rid of it themselves and be considerate people but no dice. I talked to multiple neighbors and they're fed up with it and made complaints via letter and sent emails to the HOA. I called the HOA hotline and spoke to someone directly who said they are aware of the problem and "trying to fix it", and that it was against deed restrictions and a nuisance. However that was over 2 weeks ago and nothing's changed, and I've heard that the HOA is slow about dealing with issues.

I then called in a noise complaint and Harris County non emergency police said there isn't anything they can do, because it's outside of city limits and therefore technically legal, and they don't enforce HOA laws. I said well it's legal to have a dog but if it's barking all day/night it's a noise nuisance right? They said they don't enforce any noise complaints unless "it's a party or loud music related." I feel like I've hit a brick wall in trying to deal with this issue.

Is there anything else I can do?? I don't mind occasional loud parties until late, people are allowed and welcome to have fun. Normal noise during the day is fine. But this is too much. Any advice?