What video card do you have? Either way with the right drivers there should be an option to Clone Desktop, If you can find a way of forcing that option only for those emulators that need it.
Also it may be worth you having a look at Displayfusion, this allows changing of the primary monitor on the fly with a few mouse clicks, I am sure you could setup some kind of macro that could be called.
Failing all of that do other emulators have an issue with coming up on 2nd screen, if the answer is no then just make the back screen the primary screen. (Although I assume that would mess up FP/VP if you are using them).
Last but not least if you can find and use Pete's D3D Plugin for espxe that should have an option within it for which device to use for display.
It may be that different plugins will have the same functions. See
http://www.pbernert.com/html/gpu.htm (Wow that's a lot of GPU plugins).
Sorry that I wasn't much better assistance, video card details are really needed to advise further.