OK, that was very odd indeed;
I swapped round the cards so that the card I've had for 1.5 years was in the 2nd slot and my newest card was in the 1st slot, and my computer suddenly recognised that there were 2.
And then I applied the patch and it worked! Yay!
So I can now confirm that Nvidia 310.90 work with two GeForce GTX 560s with an AMD motherboard and CPU.