If you read at the bottom of the section "Unlocking the Shaders" in the TechPowerup article there is a line
"If you get an error like ID mismatch or Could not erase ROM, then you'll have to do some extra work in a Windows command prompt (or DOS): Run atiwinflash -unlockrom 0 followed by atiwinflash -f -p 0 bios.bin where bios.bin is the path and filename of the HD 6970 BIOS you downloaded. "
There is a link to the instructions on how to do it.
Make sure your bios switch is in the #1 position.
I unlocked my Sapphire 6950 to an Asus 6970 @ 890 / 1375.