If I manually lock the PC (<Windows Key> + L) then the problem does not occur. I see a violent set of Windows mode changes, but when this has finished the screens are set up as before. I classify the effect as ugly but not catastrophic.
If I let the screen saver kick in, which results in the PC being locked, then things go screwy and on the login screen the DL monitor is now a mirror of the desktop; except the desktop now has the width of the DL monitor and whatever is a sensible height for its landscape layout.
I still suspect this of being random. I'm sure I've let the screen saver kick in before and not had an issue when unlocking.