Having it on both monitors would be great but I would also be happy to have it on a fixed monitor, so your eyes don't need to jump, or at least on the monitor that has the mouse.
(for the mouse part, I found this bug, but with little activity and older compiz. I'm using 12.04, compiz 0.9.7.12-0ubuntu3)
I want to propose yet another workaround, but for which I need help, namely, to use the "Place" compiz plugin that seems to be able to force placement on the monitor with the mouse. But to do it I need the Class of the Static Switcher window, how can I find it?