However, a reader kindly sent me this version, which confirmed that my own leadsheet was about right.
When you analyse it, Weeping Willow Blues turns out to be a very interesting and unusual jazz number.
For a start, if you listen casually, you may think the main melody is a standard 12-bar blues. But it is not.
On the recording, we begin with a four-bar Introduction (let's call that [A]). This is followed by a sung Chorus of 12 bluesy bars ('I went down to the river.....'), but they do not follow any of the conventional 12-bar blues chord progressions. Let's call these twelve bars [B]. They are followed by that four-bar Introduction [A] again (so we now notice that [A] actually comprises nothing but the final four bars of [B] - but without the vocal).
So in effect we have a 12-bar song [B] with its final four bars repeated as an instrumental tag [A]. These sixteen bars are in the key of Ab; and we usually hear THREE of these sung choruses in succession (with room obviously for additional improvised choruses by the bandsmen).
Then comes a big surprise. There is a key change to Db; and what follows is not any old melody in Db. Let's call this section [C]. It's a full 20-bar recitative such as you might have found in a nineteenth-century opera; and the first 16 bars of this are entirely on the chord of Db, with the band playing stop chords against the singer's recitative. Only in the final four bars is there a glorious resolution, with the band fully joining in.
So the basic sequence of musical events (to which may be added instrumental improvisations on [B]) is usually:
[A] = final time before [C] optional