This gives you a 17A requirement for each card. Depending on your processor, you'll need another 13A (i7-9xx series) just for that. If you have one of the newer i7s or a dual core AMD or Intel, your CPU will have less of a power requirement. You also need additional amps for other devices getting power from the 12V rail (ie fans).
You'd be safe with something in the like a Corsair 650TX (53A) or higher. If you're OC'ing anything, go higher (HX/TX/AX 750 or 850).
Generic power supplies, like the one you list, tend to leave you with too little on the 12V rail.
If you only have 40A available on the 12V, you'll need to get a better power supply to run the 2nd card with any degree of a heavy load. Otherwise you'll start to get some issues when the graphics demand becomes high. In addition to Amps, you'll also need to look for the available wattage for the 12V rail. With that processor and 2 cards, you'll need 525 (200+200+125) available just for those components. Again, the Corsair TX 650 would get you there, though I'd recommend a TX/HX/AX 750W.
You spent good money on those 6970s. You don't want to throw it away because a bad generic power supply ruined them.
With those 2 cards and the 3 monitors (and a new PSU), that will be a great Eyefinity gaming setup.
You have two 12V rails one at 25A and another at 35A! Plug the new card in and have fun! You may have to re-install your drivers for crossfire to work correctly. Every time I changed any physical configuration with my crossfire setups, I had to. Be sure to use the 'express uninstall...' option when uninstalling the AMD catalyst control center and drivers before re-installing.