I quite like the Coltrane version of the song, although Rodgers was known to have mixed feelings about jazz (and swing) musicians' renderings of his songs (cf. "I Like to Recognize the Tune"). However, I don't think Coltrane so much buries the tune but enlarges it and upon it.
I had never heard of Stifter before your post, so thank you. Oddly, your description reminds me of the giant aerial shots of the landscape (with snow, without snow) that begin TSOM -- a device Wise and his scenarist, Ernest Lehman, had used a few years earlier for West Side Story, but Lehman thought it was good for a second visit to the well. At the end of the movie the von Trapps elude their (admittedly paper tiger) Nazis by escaping across the same spectacular landscape.