The solution turned out to be pretty easy. Looking around at relevant bicycle porn and instructables.com I saw many "messenger bags" come with two straps, one goes around the shoulder and the other one around the waist.
My bag already had some wee leather straplets riveted to the sides, waiting to make good use of themselves. So it was just a matter of finding an adjustable strap with snaps in both ends. Not ever throwing anything away pays off once more. Note strap around waist below.