Thanks for all of the great suggestions.
I've ended up purging and reinstalling the 11.6 ATI drivers, pulling the 4830, and modding my overclocking settings to (so far) fix the problem. I'm going to run with a single card constantly for a week or so and then slowly mod the overclock to see what I can squeeze out of this config.
Right now, I'm just running the 5970 at 800 GPU / 350 mem. I had originally been running it at 850/300 and I suspect that may have been the culprit as once I changed the settings, it started working fine.
Thanks again for the ideas and assistance.