Hi Antony,
I can give you my experience, as I had the same machine as yours.
In my case, changing the GPU did not solve the problem, it changed it. I think the new cards they provide for service are flashed with an update (because the problem changed), but it did not fix my problem. I was having the artifact issues - to the extent where it would lock up my machine), and after the new GPU was installed the artifacts did go away but they were replaced with flashes/blinks of the screen - these looked like what would you would expect to happen to old TV sets if you dragged your feet on the carpet and touched it - white horizantal lines flashing across the entire screen. They would go from every 5 mins. to extream cases of every 45 sec.
Further through my experience, they changed every servicable part on my machine to see if they could stop this, LCD panel, power supply, hard drive, motherboard - nothing solved the issue. This was all with a clean install, no added software.
I made many trips to the Apple store and was patient and persistant. They resolved the issue by replacing my machine with a new generation (thin) iMac of the same specs.
They had to for two reasons, even though my machine was off warranty. 1) Since I paid for the first repair - the GPU replacement, they were obligated to solving the problem and 2) There are basic consumer protection laws that state that the item you purchase, regardless of warranty has a reasonable life expectincy - more or less a computer is expected to work for longer than 1 yr. in a fully functional state.
So, my thoughts would be to check your states/provinces consumer protection law, and have the repair done. If it works your good. If it does not, be persistant to require a resolution. A company of Apple's size and reputation will do right by you 9 out of 10 times.
Good luck.