Flashing the 6950 to 6970

Only the 2GB editions of the HD6950 are able to be flashed. That's all I know on the matter.  

Also, I'm running a GTS450 1GB card which is very similar to your GTS250 and I manage to run all my games (anything from Battlefield 1942 to Battlefield Bad Company 2, to Total War SHOGUN 2) on high settings without any performance issues at 1920x1080.

Current batches cannot be flashed to HD 6970s. I think the supply of 2GB HD 6950 that were flashable dried up sometime back in May.

True, most new cards do not have the switch, and those who do, it has been disabled (it does nothing). I do not know if there is a way to still do it (i guess it would be) but the chances of successfully flashing it are minimal now.