If you're using headphones then you might be best bypassing the Bose altogether? Did you try that weird HDMI port trick you linked to with the guy using g-force to push it back in?
Anyway, you shouldn't have to do weird stuff to get your PS4 working properly. I don't know why I thought you should've tried another TV now. I guess all this tech just gets too er, technical? So many things that can go wrong.