Not sure I understand you, Fink. My attached image shows the details of the monitors: Left monitor is 2, right monitor is 1 and DISPLAY shows 2-1 as the configuration.

If I switch the monitors in DISPLAY to be 1-2 (image attached)ipiccy_image 1-2.jpg, all the icons are switched but left monitor remains primary. Interesting the IDENTIFY numbers on the monitors do not agree with the DISPLAY numbers. Also I have to move to the right on the center monitor to get onto the left monitor.