Many thanks! That solved it. Ironically, I had come across that setting after I'd more or else given up. I had just set one layer to 24" spacing and the other to 16" spacing just to get some sense of the desired stagger. When I saw that setting hiding away on the Structure tab (instead of inside the Wall Types design panel itself where it arguably ought to be), I didn't see the expected result.
Following your advice, I reset both layers to 16" spacing, checked the "Stagger Multiple Framing Layers", and got the desired result.
I appreciate the very rapid response and good solution. Nicely done.