I'll chime in a bit with my VERY limited experience. My pond is about 1.5 acres and I have CC along with BG, HBG, LMB, BH, GSF & the infamouse WCP. I like CC fishing and mine are pretty easy to catch. The big ones will eat some of the bigger BG, GSF and even the WCP though. But I don't see it as a problem.
You can also try getting some fish food, Purina GFC or Sportsman's Chopice Trophy Fish Food and throw that out once a day at the same time in the same spot for a week and see what comes to it. I didn't realize how many CC and BG I had till this last week when I started feeding them at 8pm every night. Just a thought. Good luck!