Are you using a full 6970 BIOS or just unlocked shaders?
Have you tried the recommended method of opening your BIOS in RBE and ticking the unlock shaders box and flashing? You will have a much better chance of it running with unlocked shaders and everything else stock.
I promise nothing though. It's a gamble. Some GPU's might have been crippled to 6950's for a reason. Perhaps your particular card has a flawed chip, and when unlocked it just doesn't work.
if you build it, they will hate