GTX480, driving two monitors. Swap the GTX480 for a GTX970 and one of the two monitors doesn't work. Tried installing/reinstalling nvidia drivers, tried swapping the 480 and 970 back and forth.

Generic PnP Monitor driver is used to detect & install Driver of External Monitor attached to it. Working fixes for Dell, Samsung, etc. here in this post.

If Windows cannot detect the second monitor after waking up from Sleep mode, then here some working solutions to help you fix the issue.