@DABhand i was speaking from experience on my end of the 965BE my friend has it as well and no problems more problems i see these days are more GPU related than cpu and i have no idea what problems you mean about stability i think the stability problem more between the chair and the computer
As for the GPU your best going for GTX 560 its on par really with the 5870/6870(6870 is a bit slower than 5870) mind you the price of them is a good 200 at best