My dude, you are extremely passionate about this topic. Also, as a mod, you are content arbiter of your sub. Chasing people onto other subs and then claiming they're harassing you is where this fails. It works conversely as well. Many a sub has been started by disgruntled members who left another sub.
Getting someone in trouble for lying on a social media app is going to be harder than you think. News sources get approached by all kinds of people claiming to have news. That avenue is not going to work.
I am not a lawyer, but you should seek out a lawyer to determine if you have a legal leg to stand on here. Does this guy have a lot of money? If so, he may come after you if he has a legal leg to stand on.
My real advice is to protect your sub. Stop there. I couldn't stop neo-Nazis from spreading lies on reddit, and you're not going to be able to control some air purifier salesman. Just keep them away from your sub, and let it go.
By the way, this magazine you're posting on is full of a bunch of people who have left reddit. Coming here to complain about things happening to you on reddit is not going to get you a lot of sympathy.