For what it's worth, running *any* multi-monitor gaming setup, whether if it's Nvidia's Surround or AMD's Eyefinity, both setups have the same basic requirement: get as much GPU power as you can afford. A single GPU can certainly run the setup, but depending on what your overall resolution is, the games you play, and what settings and/or mods you choose to utilize, your gameplay experience may be sorely lacking due to any single GPU not being able to keep up.
From your poll, I would definitely choose the 6970, but if I had to add more to it, I would suggest running at least two of them in Crossfire to have an appreciable gameplay experience - especially if you are targeting using three 1080p monitors for your Eyefinity setup.
However, herein lies a conundrum: if you use Crossfire, you are likely to need a new power supply. But if you upgrade those components, you may be held back by your CPU, which then may require switching to a whole different platform. It is a never-ending cycle unfortunately when it comes to multi-monitor gaming - at least when it comes to getting the best performance possible.
My suggestion is to see if you can physically try it out at a store or friend's/family's house, if possible. You may end up not even liking it, as some people have had to find out the hard way, unfortunately. If you try it and realize you do, in fact, like it and really want it, be prepared to do some significant overhauling to your existing computer.
Just my $0.02.