Bob: I am very biased in favor of using multiple types of filtration and lots of fresh water. From other posts, I know your pond is around 8300 gallons (U.S.). You are changing 10-12% per week. The pond is not over-stocked (But you end up with 11 30+" koi, watch out!
) So, given my biases, I would like to see a mat-based filter or moving kaldnes or a foam fractionator added to give more variety; and I'd like to see water additions increase to not less than 25% per week and preferably 35%. Having to choose between the two, I would go to 35% per week water changes. If you can do daily trickle of 5-10% (35% - 70% per week), all the better.
The key thing to remember about water changes is that the goal is to maintain stability of pond parameters. If the deterioration of water parameters is quick (as in an over-stocked situation), then a single big water change has a roller coaster effect on water parameters. It is far better to do several smaller water changes in such a situation. Also, if the source water is being altered before going in the pond, care has to be exercised in regard to the flow rates of the altered water. Again, a continuous trickle is better.
Now, as to my choice of water changes over added variety in filtration: First, because I know you really care about your koi, I'm assuming you are getting effective nitrification even in heavy feeding periods. Second, in over 40 years of keeping aquaria, I learned that nothing did as much to give good results than large, frequent, regular water changes. Until a few years ago, I had a very low-tech pond that was very labor intensive to maintain. I nonetheless had healthy fish that grew quite well. (Not high quality show fish, mind you.) I did 50% weekly water changes as a norm. I kept close watch on my water to be sure this was not too much. There were periods of heavy leaf drop, etc., when mid-week water changes were needed to avoid too much deterioration from tannins, dissolved organics, etc. The pond parameters were kept virtually identical to the source water. Filtration can control the most toxic wastes, but does not eliminate nitrates, pheromones, hormones, dissolved organics, etc. and does not replace the mineral content consumed by the bio-processes of the pond.
One concern: The algae on the pond walls adds a dimension to the pond dynamics... a positive one IMO. Water changes result in the algae becoming exposed to the drying atmosphere. The algae can be killed off in the top zone of the pond wall, especially if exposed to the sun during water changes. This would impact how much water I would be willing to change at one time. (BTW, ever notice how after a water change the koi graze more heavily on the pond wall algae within a few inches of the surface than is usual? The drying effect of the air exposure during the water change seems to make the algae more tender and tasty... perhaps a bit like the dried seaweed collected in Japan is better dried than fresh??)