Is there a reason why you can't just add a second cheap graphics card to drive the two non gaming monitors?
You can find a card that will use any pcie slot, even a X4 slot or a pci slot that will work.
A minor advantage is that you gaming monitor will get the full set of resources from your gaming graphics card.
If you are otherwise satisfied with the gaming performance of the GTX570, that is the way to go.
If you want more performance for gaming, then you need to make it a biggish jump. Otherwise, you may be disappointed if you don't see a big improvement. That means either a GTX680 or 7970, either of which will attach three monitors.
The third attachment will need to be via HDMI, so verify that your new monitor has that option.