Hello Guhndahb. I've had this bug too, but I don't remember exactly how I got around it. I recommend two things:
1) Try an earlier save than the autosave or your most recent save. It's annoying, but it tends to work.
2) Turn down your game graphics settings to the most minimal level possible until you get past that section. Also try to turn off programs on your computer running in the background if you can (minus your virus checker, because you should always have that working unless you are not connected to the internet).
Hope that helps!
@ RC-0006 Raptor: Thanks for the links! I'll try reinstalling KOTOR at some point and see if it works.