This might be inefficient, but as well as opening the airflow and raising it, you could also buy a cheap / silent electric fan and have it blowing on the PS4 during those intensive games.

Also, my PC is quite loud and gaming with headphones blocks it out nicely

if someone wants help, my advice is don't give them it. Ha! sad but true, if you're to helpful, some people take advantage. Whoever you built this PC for sounds like one of them. I always have a ready excuse when interacting with that type, and if they're to pushy "do it yourself" followed by a bla...