Hmmm... A few trains of though.
1. I get a feeling there might not be a software solution to this. Like the others, I had a monitor (proper monitor, not just a HDTV in use as a monitor) and when connected via HDMI on a AMD card, it would always jump over to HDMI AV instead of HDMI PC. Could only correct it via physical manual control on the monitor itself to switch back to HDMI PC (finally resulted in monitor buttons no longer working after constant usage, so not really advisable this method).
I did however solve this via switching over to DVI again, which gives me a clean signal for the screen, even in mismatched resolution setups. 16:9, 16:10, 16:9.
So your possible solution (if there's no more elegant method), is to grab 2x DP to DVI adapters and connect that way. Probably best to try one out first before grabbing another.
Overscan control in my example would have been no good and only resulted in a slightly blurry and smudged screen look as the monitor and card were both re-rendering the screen. (Screen zoomed in in short, and then the card shrunk it down to compensate)
2. The other train of thought is that if your setup occassionally happens and not all the time, might suggest something similar to the above, but possible bad contact and resulting in CCC constantly switching the signal (from something like HDMI AV to HDMI PC for example).
So you have two things you can test out first to see if things improve. Although I'm going to lean on the former (use of DP to DVI being the better and likely only solution, hope I@m wrong though)