Tadpoles are not increasing the bioload, unless you are throwing in extra food for them. They are eating and processing what is already in the pond, not bringing in extra nutrients. Large numbers of tadpoles does not mean more frogs. Your 'trillions' of tadpoles could be the result of just a few clutches of eggs. There are just more survivors than you are used to, probably due to there being plenty of food for them (algae and uneaten fish food).
Tadpoles are harmless to your fish, and the koi are probably eating large numbers of them. As others have said, your best bet is to just leave them alone. Adding predatory fish will cause far more trouble than the tadpoles ever will; for example, if your koi ever try to spawn, the sunfish will gobble the eggs and fry.