SOLVED!
I feel like an idiot, but solved my problem simply by reseating my card. Can't believe I didn't try it before, but I suppose the fact that it worked so well in some games just threw me. Complete answer is copied below, Link Removed due to 404 Error:
Well, I've solved it! Unfortunately it was the last thing I tried (edit: thinking about it, this is sort of inevitable as I didn't need to try anything else afterwards, but you know what I mean).
Noticed that GPU-Z was indicating "PCI-E x16 @ x2". Ignored it before, thinking it was something that I just didn't quite understand. Thanks to Google, I worked out to reseat my card and it popped up to "@ x16". Now running MW2 at around 40FPS with my settings (depending massively on the scene complexity, obviously, but never dropping below 30FPS).
So after about 10 hours spent trying different drivers it took 10 seconds to pull and reseat the card and all was well. Ah well, am ridiculously pleased to have got there in the end. Just goes to show - never ignore the basic options. Just wish I'd tried them in this order myself:
1) Check that card is running at full speed in 3D games (via GPU-Z)
2) Reseat the card (and check GPU-Z)
3) Put your BIOS to fail-safe settings or reset by removing battery
4) Try various different drivers
Presumably MW2 highlighted the issue because, for whatever reason, it relies on that PCI interface more than most games.
Hope this saves somebody else some time, anyway.