Wait so you actually prefer your amp speaker than headphone?
Buy new headphone cause amp speaker are really not made to fully transcribe low to high frequency correctly. You are just butchering the song to make sure that your guitar stand out in what you are hearing.
Yeah, I run Rocksmith through my PA. Sounds just like a real band with it, me on bass with amp and my wife on guitar with amp kicking it multiplayer at near club volume.