Put a Sunfish in Your Pond.
This might seem like a crazy idea, considering that the sunfish is a small predatory fish, but sunfishes count parasites (along with other small fishes) in their menu of preys, so perhaps if all your Koi are big, then the sunfish would only feast on the parasites and other non-Koi organisms in your pond. However, do not put a male and a female sunfish (or plenty of them) because, in the absence of other predatory fishes, sunfishes tend to multiply in such rates that your pond will become overrun with small, malnourished fish. This situation, referred to as “stunting”, produces poor pond conditions and an imbalance in the fish population.
So start off by “experimenting” with just one or two, maybe several male sunfishes at the most.