I went through some trial an error with my first 7970 and I think 12.3 was the first version I found that worked. 12.4 is more stable, though. I have a rig with 5850s and 7970s and 12.4 (and the SDK that came with it) was the least 'problematic' to run both.
So you didn't install AMD APP SDK, just the AMP APP SDK Runtime that came with Catalyst 12.4? I'm really glad someone's had a similar situation. My rig will have a 7970 and a 6850. It currently just has a 6850.
EDIT: It's working beautifully, now (similarly to how it runs whilst in linux). Thanks

(Installed Catalyst 12.4 with its included AMD APP SDK Runtime (I did not install a separate AMP APP SDK))