I've since heard the Esher demo by George, (thanks 2-o'!) and am convinced that the Beatlles would have done a much better version. Though some of the Beats may have recorded it with Jackie, it still just doesn't have that polish, or something. Maybe they were just doing it as a friendly quick knock-off.
However, as I've listened to Jackie's Lavender Dream
tune from '72, I can tell now that a major aspect of that song's appeal for me has everything to do with Garth Hudson, The Band's keyboardist. To me the guy was a genius on a Brian Wilson scale. I believe I'm correct in stating that he was the one that put the final touches to most all the Band's recordings, and he sure did his usual high-end handiwork on this tune.