Fortnite Question - PS4/ Switch

My son is into the game, and has been begging me to play the game with him. He plays on his Switch, while the PS4 never gets used. Figured I'd give in and get into his little world with him.

Somewhere along the way, I created an Epic Games account. Under that account, we downloaded Fortnite and used his login credentials. When he's logged in to his Switch account, it obviously kicks him out of the PS4 (and vice versa).

I checked it out online to see how to remedy the situation, of trying to log out of his Fortnite account...which apparently isn't so easy. The process I went through had me logging out of the Epic Games account (which apparently is a big deal?), but even still - I can't seem to log him out of Fortnite on the PS4.

Any idea on what needs to be done? Do I have to wipe out the PS4? It wouldn't be the end of the world if so, because there's nothing on it.