I have the GTX670. So pretty much the same.
When I go to Edit>Preferences>Playback I see:
When I select the monitor I am not currently using for Premiere Pro, the Program Monitor shows up full size at 1920X1080 in that monitor.
While that may not help you, at least you know a similar card can do the job and you know that it should work.. What happens if you drop down to two monitors? Will it work then?
Also, have you performed the hack that allows Premiere Pro to use the card since that card is not in the file? I have no idea if that is relevant at all, by the way. It is just an attempt at getting our systems to work the same way.
Yes i have the hack. Im thinking it has something to do with nvidia surround. I think surround might be turning the 3 monitors into one monitor at 5760x1080 and its not showing up because that resolution isnt suported. Ill tinker around with that and wee what hapens.
I don't know what nVidia surround is - yet I have all three monitors working as expected. I suspect it's for immersing yourself in wrap-around vision for gaming etc - which is not how Adobe uses multi-screen.
As Stephen indicated, you should have all three listed in the Preferences/Playback when the 680 is installed without further bells and whistles.
Try disabling/uninstalling nVidia Surround and doing it again.