Okay I seem to be getting some headway here. I just installed the most up to date driver for the 280x, from 2/10/2017, and it has actually deactivated my second monitor and the second graphics card -- which now apparently has NO drivers installed for it, now.
It seems to be that the driver for the 6670, installed through the Catalyst installer, is forward compatible with the 280x, allowing me to use both monitors, but does not work with OBS studio. With the new 280x driver installed, I am once again able to use OBS studio, but it is apparently -not- backwards compatible with the 6670, causing it to have no driver and thusly my second display does not appear.
I think if I am able to have the updated driver for the 280x as well as the 'old' driver for the 6670 I would be able to have access to both monitors AND be able to use OBS studio, unfortunately I don't know how to do that or if it is even possible.