Well, whaddaya know?  Serves me right for never having paid maximum attention to the Miller bands. Anyway ... this tune certainly was not a staple of BLACK (big) bands of those years. Offhand I am only aware of a version of Pistol Packin' Mama by Louis Jordan (on a Jubilee program, but he never recorded it commercially). 

Yep, this one’s been in the works for quite awhile.