Although it's not ideal, I wouldn't sacrifice the extra ceiling height just to make it go to the end of the window. I think once you have furnishings in and the lighting it will be okay. Be sure to paint the entire ceiling one color so the vertical part will not stand out. Your window treatment might make a difference, too. A valance above the window would highlight the fact that it extends past the room, but drapes on each end, shades inside the frame, or nothing at all would be okay.

Just an unrelated question, but what's the end of the steel beam resting on? I can't tell from the photo. Is that more steel framing over and around the windows? Just interested.

thanks windows are Harvey and are fixed. Yes it is more steel frame goes all the way to foundation wall