I see mrsclem started the actual conversation that should be taking place; the GENERAL rule of thumb is 1000 gallons for ONE koi and 250-500 gallons for EACH ADDITIONAL fish. At 15'x9', figuring 3' deep minimum, that gives you 3000 gallons. You'll HAVE to figure out if my 3' depth is actually true. So, IF 3000 gallons, safe fish load would be in the area of 9 adult koi. You can see how you're going to need a LOT of filtration if all the numbers are correct. Any less depth and you're further across that line. If 4' depth, that gives you an additional 1000 gallons and possibly 4 more fish. So, you're right at that line. Hence, filtration is important in your case. I'd NOT shut anything down until you either build a bog (correctly sized at 30% pond volume) or accept you're going to need everything you currently have and YES, you'll need to run it 24/7. The good bacteria will die if you don't and this is what's keeping your water life-sustaining.
Again, read about bogs, make sure you're comfortable and understand exactly how they work. As addy noted, it can be relatively inexpensive or you can go the aquablox route and it'll now get pricey. I did a hybrid, sorta, of the two. The idea here is you will only need ONE pump an not have to clean anything. All you'll do is periodically thin out the plants, which will be at the top of your bog, pulling out nitrates while the pea gravel serves as your biofilter and converts the ammonia into nitrite and then into nitrate.