Our .5-acre pond is new (late 2008). In 2009, we stocked 50 CC. DH also brought home "some perch"---he can't remember which two species---

that the Department of Wildlife guy gave him. Thanks to numerous rains this spring, we have been full to capacity and most of the time, we've had water going over the spillway. I feed AquaMax twice a day, my CC look great, and the sunfish are plentiful.
OUR GOAL was to have a nice little pond for CC and LMB. I did stock a dozen 4-6" (I think?) LMB in April, but I stronlgy suspect they went over the spillway in the subsequent storms.
Problem is, the rains have been a blessing and a curse because of the upstream ponds. We have what I consider too many bullheads...and at least three carp (yellowish looking)...and I'm pretty sure at least one grass carp. The bullheads and the common carp join the CC at feeding time.
Memorial Day, a friend and I fished about 8 hours and caught 40 bullheads

(mostly very small), which we pitched onto the bank. We've had two big rains since then, but the runoff has stopped for now. She and I are going to fish again July 4 weekend, and I think we need to pitch all of the bullheads again.
Is there any reason I shouldn't? Also, if we can catch any/all of the carp, is there any reason to keep those? I'm just trying to restore some sense of balance and quit wasting good ($$) fish food!