I can’t emphasize how much this is the answer. Document your annoyances, document other peoples complaints, document the times you have tried discussing it it with him, and document how he responded. Document the fuck out of everything, because if you are his supervisor, this is going to blow up in your face no matter what you do and you need to be building yourself a blast shield asap. This guy is obviously very manipulative and portrays himself as the victim. When the shit finally hits the fan, he is going to sling it everywhere, and as your direct report, it’s going to pile in your lap.
When you take it up the chain, you don’t even have to take it up as a complaint. Ask for help and guidance in a situation that you fear is going to go bad. You have a guy who is a really good worker, but you fear his antics are going to run off other employees, or even worse, result in HR complaints.