Before the carp problem is alleviated, also make sure that you Activate any hunters or rangers that migrate to the area. They have a tendency to try to beat carps with their crossbows.
Wall around a few safe pools, for your fisher dwarfs, for times when you are not expecting liasons, or caravans. The pools filled them nasty boogers, can be utilized later for dwarf fish traps. Dig out a large area near the pools, with a floodgate to control water entry from the pool.Connect the floodgate area above ground with channeling, then once the floodgate is connected to a lever, pull it to drain the carp pool. Adding a tunnel from the drained pool, to the river,with another floodgate, can add fresh meat,bones, and leather to your inventory. Then send out the marksdwarves to finish off the rest of the finny monsters