I've been playing the carp game for years. If I were you, and if this was an option, I'd pump the pond dry and kill it off and start over. They absolutely destroy the bottom of your food chain and it's very difficult to gain much from that point on.
Also of note is that I read a study from Minnesota that ponds full of BG have 11 times less common carp reproduction than lakes that don't. The theory is that they forage on carp eggs and larva. I'd assume this is true with PS as well.
My experience in a similar sized pond was that I controlled the reproduction. The problem became that carp are such long lived fish, that even if you stop reproduction completely you'd need to rid the pond of all adults. And that isn't as easy as you'd think. In fact, I'd say it's nearly impossible.
If I were you, I wouldn't fight the battle I've been fighting for 20 years. I'd kill it off and start over.
