one of my systems running differentSLI auto is very similar to yours.
970 chipset with X16+X8, Phenom 965BE, 8gb ram, 750 psu, 2 gtx 560's and it runs bf4 flawlessly. the only real difference in our systems is your mobo is x16+x4 pcie. Do you have the card in the X4 slot dedicated to physics? and does it run any other games without issues?
I don't have the card in the X4 slot running physics, I just have it set to run in SLI with my main card. My system runs BF3 fine. I also switched my SLI bridge around, got all my games to work BF4 too, but had green artifacts all over my screen no matter the game. I am doing further testing now too.
Edit1: No matter what I do on 337.88 drivers, game crashes everytime, updating to 344.48 now
Edit2: No matter what I do on the newest drivers 344.48 I still can't get bf4 working with SLI enabled, fine with the card dedicated to PhyX, but now BF3 is hard freezing too, causing the same problem as BF4
Edit3(Final): I now can't load into any games, tried drivers 337.88-344.48 can load the single-player fine, but not the multiplier. It freezes my PC, but if I leave a video running I can hear the video, its like my pc continues to run but my monitor shuts off. Tried increacing CPU voltage and gpu voltage but nothing. Really starting to lose hope for SLI. For now I am running my other GTX 560Ti as a PhyX card only disabling SLI all together until a solution is found.