I am new to this whole "trophy catfish" thing, so I began using cirlcle hooks back in June. All my life when I fished for regular ol' cats I was using small hooks, small bait, and I had a lot of throat hooked fish. Back then the hooks were #2 Eagle Claw hooks that you found in most tackle stores with the leader already on them.
When I began the "big bait, big hook, big fish" approach for catfish, I also began using circle hooks. I have caught close to 300 cats with circle hooks, and so far I have had two that were hooked deeper than their outer jaw. When this has happene I simply cut the line close to the hook.
I did read some research that showed that cutting the leader close to the hoko may not be the best thing. I said that leaving leader exposed actually helps to keep the hook flat when the fish swallows food.
On the same note, I did catch a nice 6 1/2 lb. cat last week that had a hook with leader/swivel attached extending from its anus. The leader and swivel had made it out and the hook was still inside. I gently tried to pull it out, but there was some resistance so I cut the leader off close to anus and let him go. I would assume the barb and point were rusted off becasue I doubt the hook made it through with the barb/point still intact.