2 750 watt power supplies might give you more connections for the 7 video cards, of course a solid 1200 watt or 1300 watt would do nicely also.  I think my coolermaster 1200 watt has enough connections for 4 video cards but it doesn't have many regular power connections for fans, etc which you will probably need to put adapters on to power the video cards.  That is with each of my 4 video cards using 2 power connections.

If those 270s only require one power connection then you might be ok with a solid 1200 watt power supply but 2 750 watt power supplies might even be around the same price or cheaper and would work pretty well.  If you want a little headroom then you can go with 2 750 watt power supplies.

of course I kind of actually prefer the idea of 2 750 watt power supplies so you aren't continuously stressing the power supply so much.  I had an 850 watt antec burn out on me a few weeks ago with just 2 280xs on it.  So for long term use I would probably stick with 2 750 watt power supplies.