Looks like your jamb depth on the new door should have been 6-9/16" or 5-1/4" - not 4-9/16". That extra wood piece in your picture was probably added becuase the person before you made the same mistake and tacked on their own exterior jamb extension to get the brickmould to cover. You're gonna need to do the same thing. You could do your quarter round idea or something similar, but from a professional's viewpoint - yikes.