BK, in my various jobs digging into 1930s musicals of Cole Porter and Richard Rodgers, it's my observation that when it came to the "ballets" in their shows, they actually composed the music. It was the dances that accompanied the songs that were arranged by the orchestrator or his ghostwriter. So, Rodgers composed "La Princesse Zenobia" and "Slaughter on 10th Avenue" for On Your Toes, but another did the dance arrangements for "On Your Toes," "There's a Small Hotel" and other songs. Unlike later, he wrote out the entire scores.
"The Carousel Waltz" was actually a suite of waltzes he wrote in thew 1930s and I believe the orriginal score may be in the Rodgers Collection of the Library of Congress. I have never seen the manuscript, but it's my belief that the wonderful opening of the "Carousel Walt," which sounds a bit like a calliope warming up, may have been arranged by Russell Bennett, the show's original orchestrator.