check to make sure the bios number is the same across all the cards. use GPUZ to look at the bios number, im going to bet the bios number on the actual 6970 is different than the flashed 6950s, theres your problem. if the bios numbers arent the same, the cards dont like talking to each other. when i was setting up my 6950s ( unlocked to 6970s ) thats what was giving me the hardest time. i tried everything, checked the bios's, made sure they matched up, had to flash the appropriate bios on one of them and they worked ( better ). also try moving them around to different slots. you said everything was working good with the 2 6950s then the 6970 botched it. try running the 6970 by its self and see if it performs as it should.
this is the reason i went to the green team like Mguire was sayin. i sold my CF 6950s for $350 and bought my 680 on Craigslist for $350. i mostly did this because my CF 6950s wouldnt work in far cry 3, and i had been looking forward to that game for about a year. having a rig that wasnt able to play the game that iw anted to play just wasnt an option. havent looked back since. AMD will have to come out with a monster for me to switch back to their cards.
Also my single 680 performs about 40% - 50% better than my CF6950s( unlocked to 6970s )
check out my thread showing my findings:
switching from the red team to the green team
be sure to check out my post on the second page
my favorite thing about the green team is
! its awesome