jjzavodny-
I don't have all the answers, but I can definitely relate to your problem. We've had similar experiences with unstocked bullheads around our feeders. Unfortunately, that experience is normal for us, but it shouldn't be normal for anyone. I'm assuming when you say yellow or mud cats you mean yellow bullheads as opposed to actual yellow cats?
My advice would be to keep fishing for them, especially near the feeder around feeding time, since that's where they'll be. I'm sure at 8 y/o your son enjoyed catching them, even if they were only 7" long. Assuming that you don't want them in your pond (I don't in mine), explain to your son that they are not helping the pond and are eating most of the food meant for the CNBG and FHM. This way you can give him a job to catch as many as he can, and he'll understand the importance of it and have fun doing it! I'd imagine he'll catch them as fast as you can take them off. My dad and I caught seven bullheads in one cast on a leader with seven #10 hooks. I'd recommend using the small hooks and worms, shrimp, stink bait, etc. Bullhead fillets are actually pretty good, but the ones we catch that are too small to fillet make good fertilizer.
The other option is to trap them. We've had good luck so far with that, but the trap catches fewer and larger bullheads. We catch more and smaller bullheads on hook and line. The problem with trapping is that we've also caught BG, LMB, and HSB and tried about every bait I've heard of.
If all else fails....dynamite.
If you want bullheads in the pond, then ignore everything I've said...as George and Bill Cody say, "it all depends" on your goals. I'd rather use the feed and biomass on BG, RES, CNBG, HSB, and LMB. I hope I've answered your question and not gotten too far off on a tangent. Good luck!