I am also one who has HD6970 with very similar PC configuration as the original poster.
Alienware Aurora R2
I7 860 @ 2.8 Ghz
8GB DDR3 Ram
Windows 7 64 bits

Strange that before I came back was using HD 5800 series and instead of complete freeze, PoL simply crashed with the Display driver stopped responding error. I have so far tried a few methods with no avail:

- Disable HTT from Bios
- Disable Weather/Shadow from ingame
- Disabled all effects from game
- Tested Drivers 12.4, 12.6, 12.7beta, 11.2(!), it all gave same results
- Updated Realtek HD audio drivers to the latest.
- DIsabled Realtek HD audio, and used HDMI cable instead of VGA
- Changed CCC configuration to max compatibility and disabled AMD Overdrive

None of these worked. The freezes are also quite random and freezes on random areas. Someimes it froze in the first 30minuites, others lasted for 5 hours. Sometimes no issue for 6 hours straight. Strange thing is that my 2nd PC is also running on i7 with Radeon card. However its a laptop. It has HD 4870 and using a very very old driver, I think its catalyst 8 something. Now its not even funny have to roll back that far and I don't think those drivers are compatible with the 6000 series and up.

Lastly, the game doesn't seem to freeze when you are idle. It happened to me when I was moving around, fighting etc. at this rate it can and probably will damage my rig and I will probably be forced to quit the game because of it. It may not be an issue today, but with the new expansions and more people upgrading their PC it will be a problem for future players if SE doesn't do anything. (Doubt AMD will move since its one game out of many)