Controlling amphibians is not easy – but hatcheries try to control them, especially tadpoles, because the tadpoles take up space and use valuable resources in terms of oxygen, food, while contributing to waste production, for no net financial gain for the farmer.
Control: The growers try their hardest to catch the tadpoles while in the "egg mass" – these appear as gelatinous masses floating in the water with small black spheres in there. They slurp or net them up – because they know that if they don't intercept the eggs; the tadpoles themselves are REALLY tough to get out of the ponds. I saw a Border Collie dog once, that was trained to bark at the egg masses, and then they had a guy on a four-wheeler who'd come by and get the eggs in a net.
Tadpoles already hatched? Here's what some of the big growers do – they buy or catch Blue Gill or Crappie pan fish, which can also be caught in traps with corn. You want these carnivorous fish to be about the *same size* as your Goldfish, as they WILL antagonize your Goldfish, if they are small enough. Bass are worse to beat on (or even eat) goldfish and small Koi, but they work.
I've been told that (Channel) catfish work well for tadpole reductions. I don't doubt this, however I believe that the pan fish work better in several ways, or else the breeders and growers would use more catfish, and I don't know of any hatcheries using catfish for tadpole control.
If you go to the ornamental wholesale or hatchery you'll see one, or MAYBE two, three-inch Blue Gill or Crappie per one hundred Goldfish. So you don't need any kind of "school". Some people would warn you to keep only one fish per species so that you never risk them breeding – because they get violent MOSTLY if not only when they're ready to breed and protect their territory, eggs and fry. Other people have recommended some baby small-or-large mouth Bass. BE CAREFUL! Bass definitely eat more tadpoles than the pan fish do, but they also grow very fast – they will grow very fast on a diet of tadpoles and get big enough to eat or henpeck your desired fish.
So, that's what I'd suggest. ONE or two Bluegills. Or a baby small mouth bass. Remember, you *can* introduce disease on any new fish, including your tadpole regulators, so they should be quarantined just like any other fish.
PS: It's a common question whether salt hurts frogs and tadpoles. The answer is: Not at the usual 0.3% or 0.6% salinity.