Well if you read this Nov article, it talks about big cats. But, these cats were blues not channels. The article mentioned that blues were the dominate species and were eating the bass.

Now it seems to me if you are Bass 'heavy' you would want to have some help thining the Bass out. The thing to do is find out if the channels are forageing down on the Bass or are they forageing down on the Bream. If it is the Bass they are eating then, you might want to keep them. There is NO WAY POSSIBLE that you and your family can catch enough bass to thin them out to the right balance.
If they are feeding on the bream you would then need to thin or totally erraticate the channels.

Heres what I would do:
1) read that article in this latest pond boss magizine.
2) Decide if you are really Bass 'heavy' in numbers, or just have 'stunted' bass.
3) Take a sample of the larger cats and decide if they are eating the Bluegill or the bass.
4) If they are eating Bluegill You want to get rid of them...if trophy bass is your goal.
If they are eating your bass, AND you are Bass heavy, I would think again on killing off all thoes channels, because they would be helping you..

If I had to guess, the channels are probebly eating more Bluegill than Bass, being that they are channels not blues. Which in this case you would want to cull channels as much as possible. If you are not bass heavy, but have stunnted bass, that is a tall tale sign that the channels are outcompeteing the bass as well.

Hope that some of the other experts can chime in on this one..