Fletcher Henderson & His Orchestra had a hit in 1936 with an earlier (but not the original) version of “Sing, Sing, Sing (With a Swing)!” The lyrics make references to hits of the day, such as Riley & Farley’s “The Music Goes ‘Round and ‘Round” and Cab Calloway’s 1931 hit “Minnie the Moocher.” Listen to it here:
http://www.youtube.com/watch?v=5Yyk5lTFQs0
Yeah, I remember that version, too. Sounds very familiar when I listen to it now. As you say, it was 1936, not 1927 as YouTube says.
The Goodman version is partly adlibbed, as was their custom. After Benny comes in, the whole band picks up his revised theme.