Would built in dining room bench seat save you any room?
TBH I don't really like them and my OH is lobbying for one, but they do seem to save space and give extra storage... albeit not that much for you as you've got the rad behind.
Also is the piano necessary? Could you sell it to fund the big TV?
have you got a roughly-scale top-down drawing? I've got a mad suggestion but I want to doodle it before I say it out loud.