I hate to say, but get a Lawyer quickly
Had a similar situation with a neighbor. Neighbor had a defective stereo and telephone that picked up RF. Neighbor would not listen to reason. I really tried my best. Neighbor got police involved. Got an ARRL Lawyer right away.
Lawyer basically wrote a letter to neighbor (and police) telling them to pound sand. The lawyer went a step further and hired an engineer to measure RF. Easily within limits.
You are dealing with a control freak. My guess is your neighbor has lots of time on their hands. Miserable people like that seek out trouble.
It is so nice to operate with NO worry whatsoever. I'm almost to 200 countries confirmed now.
Cooperate but operate. Be polite, but be firm.