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Amd and nvidia drivers can quite happily coexist these days - we have had PCs at work with an amd card and an nvidia fitted at the same time without issues.
Writing this with the 6950 installed. I did exactly as above and everything went like a charm. Whether it still goes as easily when I got back to green is another thing entirely but so far it's all going swimmingly.
BF4 Ultrawide doesn't run very well. Had to drop the quality down to 'Medium' to get FPS even above 50. Smooth enough but not particularly great.
See if the 6950 will soft mod to 6970 for a bit more power:
http://www.techpowerup.com/articles/overclocking/vidcard/159