Nathan,
First, I agree completely with my good friend Dave D., except that I have some minor reservations about his last suggestion of killing off the pond and then including hybrid bluegill in the restocking ... more on that below.
No matter what, catfish in a small pond are both good and bad. Catfish generally cannot successfully generate new populations in small ponds for a wide variety of reasons.
The upside is that channel cats, at least in my area, are extremely cheap to stock -- even at the 12-14 inch size. I think I last paid about $1.50 a piece for 12-14 inchers. They transport very well, and they are very hardy. They are voracious feeders that grow very fast. Mine typically double in size each year.

The downside is that channel cats are voracious feeders that grow very fast. They are very smart. The become hook shy real fast, and can become quite difficult to catch. When you can't catch the smartest ones, they get to 10-20 lbs., and they can cause a lot of damage to a pond.
It is certainly a balancing act. As Dave says, they can run out of oxygen in a bluegill heavy pond.
One option is to go with a catfish-only pond that is pellet fed. A second option is to put twenty-five to a hundred 12-15 inch channel cats in your pond with the bluegill this spring, and see what happens.
DON'T PUT MORE CHANNEL CATS IN THE POND THAN YOU REASONABLY FIGURE YOU CAN PULL OUT IN ONE OR TWO SEASONS!
If after one season, you aren't catching decent catfish, and there are still lots of stunted bluegill, then I'd think about either adding bass, or taking Dave's suggestion. If you use hybrid bluegill, you will probably have to feed the catfish. Then they are easy to catch on flies and pellet flies.
Lastly, if the channel cats over-populate, call some buddies from Oklahoma, and they'll gladly come noodle the big ones out by their front teeth!
