Like Maziar already said the 6870 is a pretty good choice as well.
The 6870 uses around 140W idle and 320W with load.
The 560 uses around 150W idle and 360W with load.
Your power figures for both cards are way off, a single GTX560 uses nowhere near 360w under load as two of them would have melted my PSU by now if they did!
When i touch my smps from the very back side of it where the power cable is inserted that portion is too damn hot that its difficult to hold down for more than 3-4 scnds......amd gpu i have not checked.....but as it is written on the box that it will work on min 500W then how come it is working upon just 350W smps??????
The hot air and heating up of your 'smps' is a sure sign that it's being run a maximum, do not be surprised if it goes 'pop'.