In answer to the question if any Kennedy Center show was transferred to Broadway, the superb 1983 production of "On Your Toes" with absolutely ancient George Abbott, elderly George Balanchine and frail but wonderful Hans Spialek all returning to create their original direction, choreography and orchestrations,respectively.
I LOVED that production which had a health run on Broadway and an even longer run in the West End (which was amazing because the show lasted exactly 80 performances in 1937 in London.
http://www.broadwayworld.com/board/readmessage.cfm?thread=972787#3631451
http://www.broadwayworld.com/board/readmessage.cfm?thread=963561#3533883
http://www.broadwayworld.com/board/readmessage.cfm?thread=955158#3440952
http://www.broadwayworld.com/board/readmessage.cfm?thread=954269#3427915
http://www.broadwayworld.com/board/readmessage.cfm?thread=955012#3441622
http://www.broadwayworld.com/board/readmessage.cfm?thread=954344#3428699