Allmusic.com says THE KING AND I was written by John Gorka and Fred Koller--a one-off collaboration, apparently. As far as I can tell, John Gorka hasn't recorded it, but Billy C. Wirtz did. It's on his album "Sermon from Bethlehem," and it's on Fred Koller's album "Songs from the Night Before."

Maybe this information will be useful to somebody.