Condor,
the screen went completely black
Does this happen if you set the texture mode to 1024? I did my first 18 months of alpha testing with a 6770 1G and never had that happen in 4096 mode. At the worst, offline you should be 25-35 flying close to the town or driving around in it. Furballing with up to 5 players around you in the 40's. I have subsequently replaced that card with the beta nearly finished.
HD 6770
GDDR5 - 1G
Data Paths - 128bit
Band Width - 80 Gbyte\sec.
Shaders - 800
HD 6950
GDDR5 - 2G
Data Paths - 256bit
Band Width - 160 Gbyte\sec.
Shaders - 1408
Your DXdiag shows you have installed version 10.18.13.5900 AMD drivers for your graphics card. The latest for your 6950 are 15.7.1. If the latest drivers don't improve your FPS and make it possible to play in 4096 at the defaults. You may have other things wrong in your system.
I noticed from your DXDiag that you may have once had a GTX 750 in your PC. Is it still in your PC, if it is, remove that card if it is not being used(?).. If it is not, you may want to run an AMD\Nvidia driver wiper in safe mode and target all of the legacy Nvidia drivers still on your PC. Then update your AMD drivers.
And then it looks like your mother board has onboard video, Intel(R) HD Graphics 4600. Is that disabled? You are also showing a High Definition audio controller. Is your video card connected to a TV or a monitor with speakers with an HDMI cable? I had some performance issues doing that until I put a DVI adaptor on the HDMI cable at the video card so I could disable the HIDef audio device.
Does AH2 occasionally crash on you out of the blue during high intensity sounds and action?
And last, is your power supply of a high enough wattage to support your video card?