I downloaded the latest drivers from the ATI site and attempted to install them, then aborted the installation once Windows started yelling at me about them not being tested with the windows logo. Of course, next time I re-started my PC, I found that I didn't have graphics drivers anymore, so I was forced to install the new ones regardless.
They worked, despite me being over-cautious about them breaking my PC, so I tried turning the Catalyst AI off. It didn't work, unfortunately.

NPCs still do that weird standing still thing as shown in earlier screenshots, perhaps because even the latest drivers for my card are outdated. But at least graphics in games look slightly better and things run just a little smoother now (even though I now have the Catalyst Control Center hogging a little more memory than before...).
I think the ultimate fix would be for me to replace my ageing (7 year old) beast of a PC, and I actually feel lucky that Stranger runs at all at a playable framerate, but thanks for the advice anyway.
