Tried 8 BIOSs with the same device ID from the TechPowerUp Video BIOS Collection. Unfortunately, none of them unlocked undervolting for me. Some of them actually increases the power consumption significantly (both idle and load).

Using the stock BIOS, the power consumption of the system (with GPU load) is ~264W

HIS.HD7970.3072.120816.rom
Works, but the voltage table is exactly the same as stock

ATI.HD7950.3072.120706.rom/HIS.HD7950.3072.120706.rom (idential ROMs)
Does NOT work

ATI.HD7950.3072.120116.rom
GPU-Z reports a lower voltage at load, but power consumption increases to ~452 W

MSI.HD7950.3072.120202.rom
GPU-Z reports a lower voltage at load, but power consumption increases to ~450 W

VTX3D.HD7950.3072.120822.rom
Does NOT work

Sapphire.HD7950.3072.120706.rom
Does NOT work

Sapphire.HD7950.3072.120731_1.rom
Does NOT work

Sapphire.HD7950.3072.120907.rom
GPU-Z reports a lower voltage at load, but power consumption increases to ~320 W