Trying to use a dual-monitor desktop system with Windows XP.... 1 graphics card... with digital/analog outputs.

Picking: Desktop -> Properties -> Settings -> Identify

It shows "2" as my left monitor... and "1" as my right. How do I switch them around?

Here's what I've tried so far:

Switch the cables (I can't.  I need the digital cable on the better monitor.)
Switch the monitors (I can't.  One has a few dead pixels.)
Drag the 1+2 graphics around (That doesn't change the IDENTIFY numbers.)
Pick "use as primary" or "extend"  (That doesn't change the IDENTIFY numbers.)

Anything else I can try?
What exactly controls/switches the "IDENTIFY numbers" around?

I know it can be done. For weeks I ran this exact set-up... with the CORRECT numbers appearing on the monitors.... then just recently... after a few reboots... they now appear "switched around".