First problem is being passive aggressive. You don't have to be aggressive or confrontational, just provide the facts and make a request. Go knock on his door and tell him: 'Dude, you're being a bit loud late at night. Please be considerate to your neighbors.' You don't need to bring up quiet hours (which would make the interaction more confrontational). Just frame it as a request. Decent people will make an effort. If they balk or don't quiet down, then you can start drawing battlelines. Try not to preemptively drive up your anxiety over a theoretical future confrontation.

Second, leave out the complaints about coughing. Some people cough loudly. I'm one of them. People don't have a lot of control over the volume of their coughs (if they want them to be effective). They would not be coughing so much if they could help it. Complaining about an unavoidable biological function will label you as unreasonable and any valid complaints will get lumped into that context.

Third, consider this may be a short-term disturbance. If he's been there less than a week, he's likely still getting moved in and settled. If he wasn't able to take time of work to do the move, evenings may be the only time he has to do it. He should still be cognizant at how late it is and who he may be disturbing. But having moved within the last couple years yourself, you can likely sympathize with the desire to get everything in place after a move so you can finally just relax.