Thank you all for the advice and stories.
Yes, I realize that digging in might not be in my best interest. Never once has she asked me to get rid of him. I mentioned the “i cannot and won’t get rid of him” to give her my position on how much he means to me. I want to be a good neighbor, but I also want to enjoy my chickens. I realize that the property is smaller and he’s going to be heard no matter what. Her initial posed issue with the sound is that she doesn’t want it as close to her home.
I live in a small, rural community in the mountains of Southern California. There are 50 or so homes in this small community. Real tight knit. Everyone is really cool. People kind of operate however they've wanted. My neighbor had peacocks for years (until the mountain lions got them, & illegal), pigs (also illegal), dogs (unregistered with county), roosters (there were several in our community, now I’m the last one). The neighbor herself is currently in a similar situation. She has two large dogs who break out of her yard almost every day. Every one of my neighbors have all played their part in catching the dogs and calling them to come get them, including myself on several occasions. There have been several complaints about how they cannot contain or control their pets. When I initially had the discussion with my neighbors on the opposite side her to inquire their opinion about the crowing, there were no issues. If I do build a Batchelor coop on the opposite side, I know that my two neighbors have zero problems with him. One of these neighbors is actually the lady who was pissed off that I culled poor Buffy Brahma

“How could you?”, she said.
I’m going to have a more in depth discussion with her about whether or not we can compromise. I will explain that she’ll still hear him, just more in the distance. Get a more clear understanding of what she wants here…
I appreciate the Batchelor coop feedback. Anyone with anymore Batchelor coop stories as it pertains to temperament , please share!