Soundproofing your garage would be the best way to offer olive branches to all of the neighborhood, olive branches for everyone, yeah! let olive branches rain all over the silent place ^_^
We all will silently thank you for it. *** Sigh ***
Getting offended is the new black, and people find all kinds of ways to be offended, it adds spice to their lives. And you better not breath because the next door bloke might be "misophonic" which many people with real disabilities consider to be a made up "disability" which provides a license (prescription) to behave nasty. Regardless of you agreeing or disagreeing, you now have to deal with nasty behavior from people who think they are in the right to act crazy and make a big deal about some distant sound emitted by the natural aftermath of a person being alive. In this case, you are enjoying being alive practicing a hobby at a several yards of distance, regardless, someone finds a way to feel offended by your activities.
That said and addressing the situation you faced:
There's one thing you can thank him for, though. He might have voiced concerns that other neighbors might be too shy or "nice" to voice.
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. You really don't want to be extending an olive branch to a neighbor whose opening line to a fellow neighbor is and aggression like that:
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. 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.
Remaining calm was the best thing you could do, you can be proud of yourself. But other than that, some other answers are suggesting that you go for the submissive strategy, which is the same as treating him as your boss, your ruler... please don't let assholes rule your neighborhood, this is how they get to rule the world.
- 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 accidentally supporting the stranger, by calling the police next time the man comes invading your property and yelling.
Not being used to this type of situation you might think it's ridiculous, but the police know this is exactly the type of situation where many violent crimes are committed, i.e. a person who lost their cool.
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.)
My experience with an invasive individual was similar in that I didn't do anything wrong but the person invading my home thought he was above the law and he could simply use his presence to convince me he was right and I was wrong. It wasn't a neighbor, it was a person who had bought the property my family was occupying and he decided he no longer wanted us there (he bought it for a reason, he had plans for the land).
Disregarding the law, he thought he could evict us by simply going there in person and putting pressure on us, but we still had an ongoing rental contract. He got loud after I informed him I knew the law, but I stood my ground, after he left a neighbor came to express her concern for my life because she recognized the guy from some mafia, and while a susceptible weak person would have submitted to pressure and fear, I figured there were ways to keep this person at bay.
He kept coming twice or trice a week demanding we removed ourselves from the property and the original landlord was being evasive and wouldn't pick up the phone. A rumor came to me about him loosing the property over some stupid game. The situation felt as if it had come out from a movie script or a cheap tv show.
One day that I was not home I received a call from an awesome friend who sent the police because this stranger was invading the property, when I arrived the police was already there and this was helpful because it set a precedent with witnesses of his unlawful behavior. Regardless of how bad the discussion and the whole episode with the police with him infuriated, he had no other choice than to adjust his behavior.
From then on, the man tried to be slightly more amicably, very hypocritical though, he started to compliment my pretty eyes and face, etc. Started to invite me for drinks... besides me not being gay, I really didn't want to be friends with a mafia person, but this gesture was the telling sign that he now recognized he was not in a position to be demanding anything, the situation had changed, he was now acting submissive, willing to spend money on me to earn my favor. I declined his invitation, however, to show my good will under my own terms, I agreed to him sending a person over to start preparing the land for what he had in mind. A person with a machete started to come over and it turned out to be his brother, and his conversation had a sniff of sadness and a stroke of creepiness, hahahaha, dayum, well, whatever. The story doesn't get much more interesting or helpful for you, I simply made sure to be convincing when I lied about where was the new place my family was going to be living at.
The point is, stand your ground, use the law at your favor, exhibit the man's wrong behavior, keep the rest of the neighbors on your favor. You'll be fine.