Those are some big cats. IMO if you are limited to 35-40 of them, it's a number that can be whittled down.
Search the Q&O and Controlling Fish topics for catfish control threads - there have been a lot of discussions with lots of different ideas. Here are some highlights, some of which I have used myself successfully:
1. Utilize a varied and varying approach. Fish with fairly heavy tackle, use jugs, use a trotline.
2. Vary your baits to keep 'em hitting. Stinkbaits, liver, cut and whole fish, and more. Try the self-replenishing bait - naked catfish tails (I have had decent results using post-fillet catfish tails cut into thirds on jugs).
3. If you get the cats feeding regularly, you can throw a baited hook into the midddle of the pellets and get them there. I have been able to pull a couple of big cats a week out using this method.
CCs can be pretty smart, so you have to alternate and rotate methods and keep adding new ones.
P.S. After they eat fish feed for a while, see if the taste has improved. I have this hypothesis that eating fish feed makes CC taste better than when they are scrounging their meals.