You really don't want to be extending an olive branch to a neighbor whose opening line to a fellow neighbor is "really?!".
But now that you have the good intention to do so, at least don't do it under his terms.
This person had the nerve to come to your home and antagonize you, accepting your handshake is not necessarily a sign of good will, which was confirmed by the disgusting way he rejected your invitation for a compromise.
He thought he had won before even starting to negotiate like a sane person, you don't want to offer positive feedback on his insane attitudes.
- Extend an olive branch under your own terms. That could be expert advice from you on how to soundproof his home. Don't help him with such endeavor as that could be taken as admitting guilt and providing compensation in advance.
- Don't go to him, let him come to your property.
- Prepare a hidden camera and record his actions, recording inside your property and public spaces is permitted.
- Ask your wife to be prepared to support you instead of the stranger by calling the police next time the man comes invading your property and yelling.
You will have the footage as proof. He will be discouraged to call the police and if he does, they already know who's the problematic one.
That is, unless you are in fact in violation of some civil code, I don't think you are but it wouldn't hurt to investigate your local legislation.