If you decide to get the used monitor, make sure to test it before you buy it. The seller should allow you to test it before you buy it if the seller is legit.
If you do get the used monitor, then the GTX 670 with at least 2GB will be needed for that resolution.
If you buy the new monitor, then you can get the second GTX 570 and it should be good for a while at that resolution.
Since you say money is not an issue, then you can sell the GTX 570 and buy 2 GTX 670 for an SLI setup. A single GTX 670 at 1080p would play all games on ultra. I would get the GTX 670 as it is more energy efficient and would be less stress on your PSU.