Great post, Trelane.
Reminds me of the documentary Elvis '56 and it made the point near the end there that Elvis' final performance on the Ed Sullivan show in early '57 featured an Elvis who seemed a little more wrapped up in the image (I don't mean in a conceited way...hard for me to explain) and was more playful with the audience. He had lost, though perhaps consciously and not irrevocably, that harder edge to his performance style.
Maybe that came with a degree of comfort about his career; he might have gotten to the point where he did not have that nagging sensation all the time that he was going to wake up and it would all be gone. And that may have come through in his recordings and in the material that he chose.
But understand I am not saying the man couldn't rock anymore in '57. He might have just chilled a tad and no longer had the hunger, so some of the rawness was lost. There may also have been a conscious effort to sound more refined.