Fraser, I suggest checking a youtube video on how to reset the GPU's solder connections. Apparently, with the overheating the solder connections loosen causing the fragmented windows and then freezing. Normally one would replace the GPU assembly, but since these are extremely hard to find and costly, resetting the solder connections might be the only option to try.
At YouTube.com search for "Casual iMac Video Card Repair".
I've been meaning to try this repair for two years now . . . finally going to give it a try.