Another is a nearly-forgotten song called I Don't Know Nobody Here and Nobody Knows Me, composed in 1924 by Jo Trent and Will Donaldson. The piano music shows a 16-bar Verse in D minor leading into an 18-bar Chorus in the key of D major.
And Lil Hardin uses the minor very heavily in the early stages of Perdido Street Blues before inviting the musicians to play 12-bar choruses in the related major key.
It seems that readers are just as stumped as I am. Only two responses have arrived so far. Robert Duis in the Netherlands offers Chega De Saudade, which has a verse of 32 bars in the minor, followed by a 36-bar chorus in the major. It is a 1958 bossa nova by Antonio Carlos Jobim. I have not personally heard a traditional jazz band play it. And Richard Bogen in Phoenix, Arizona, has told me that Shine On Harvest Moon (music composed in 1908 most probably by Nora Bayes-Norworth) has a 16-bar Verse in the relative minor. I did not know the Verse, but I have found it on the internet and yes: Richard is right.