I finally got around to the proper LCM version of this. (There are no LCM pools near where I live.) This weekend at NW LCM Zones in Oregon I did a 400m fly in 5:37.45. My first 200 was 2:46.19 so my 200's were split 5.07 seconds apart. It was pretty cool. I am considering longer distances.
It was reported that Carl Robie held the Middle Atlantic AAU Regional record in the 400m Free in the 60's, having done it Fly, but I have no confirmation of that. I wouldn't be surprised if it were true, as he could swim Fly all day.