Anything other than what I've said above is speculation, but I'm pretty sure games maybe even cards or something caches things that have just been rendered or things they think have a high probability of being looked at again.
To kind of back my theory of caching play some more crysis and as you go around into new levels, engage in new events(heavy firefights) you'll notice the dipping in clock speeds more thus making the game stutter. I don't recall the stuttering a 100% as its been a while, but I feel like fast turning did make it stutter at times.
And not worth messing with the card imo, unless your familiar with it can be quite annoying/difficult due to lack of good documentation/dos boot tools.
Our setup is pretty similar,
3930k, 3.7ghz, ASUS P9X79 Deluxe, OC might have been at 4.0 or 4.4 back then. I tried messing with a whole bunch of bios settings too I think. But it was 24hr Folding@Home stable. (Stresses better than P95 or anything else from what I've seen)
780 classified, could have been a regular 780 back then or even a 770. (Also Folding@Home stable).
32GB ram 1600Mhz(?)
It was running of my 2x 128gb 840pro raid, also tried in on a hard drive in case the raid array was bad... I know.
2560x1440.
What kind of frames were you getting, I tried Master_Config and it made the game look alot better and stressed the card a bit more, which might have helped a bit. If you have a good heatware profile or live near (DC/NVA area) by I don't mind swapping you graphics cards if you want to try and fix this. The 780 classified has a dual or maybe a tripple bios which helped me a good bit in messing with the primary bios and just restoring it using the backup bios if I messed up.