Should work fine. I think the earthwatts are multirail though, so be careful. You might have power locked to rails that won't be available for your vid cards.
Got 2 5970, 2 5870, and 1 5850 (all reference) on a PSU with a single 860 watt 12v rail. Draws about 900 watts at the wall. It's only 83% efficient though, so probably still has some wiggle room.
How much mhash are you getting out of a 5970 and at what clock rate with what miner?
I've got 3 5970s and 1 5870 on a 1.2kW Seasonic PSU.
My 3 cards are clocked differently.
@ 850 engine I get 400 mhash a core (GPU 1)
@ 900 I get around 420 mhash a core (GPU 2)
@1000 I get 470 mhash a core
I've pushed one of my 5970s to 500 mhash a core but VRMs were in the high 90s and low 100s.