tl;dr even with the best filtration, you’ll probably still need to increase water changes to keep the goldfish.

*Typically if you have measurable nitrates, the ammonia cycle is where it should be.

Just a quick primer: there are specific bacteria that oxidize each form of nitrogen into less toxic molecules. Nitrosomonas oxidizes the ammonia into nitrite. Nitrobacter oxidizes the nitrite into nitrate.

Its likely that the necessary bacteria is healthy and in sufficient numbers, but filtration/flow is lacking – and this is the key point – for the bio-load in your setup. Water changes will be the only fix here.

I’d test for nitrite and ammonia just to rule out loss of one or more nitrifying bacteria. If you have measurable ammonia, you could step up water changes (frequency or volume or both), or remove the grubby, stinky goldfish.

Back in the 90’s, the local aquarium hobby store where I worked had around 1k feeder comets in a 55gal tank in the back. It was plumbed to a massive wet/dry sump that was full of “bio-balls” (the height of filter technology at the time) and pumped by a 1.5HP pool pump. IIRC, the total water volume was over 125gal. We had to change the water in that system every week to keep the water clear and clean.

Maybe its snobby of me, but it never seemed worth it to me to keep goldfish. I prefer Mollies for hardy fish, and they have more personality for my $.

Bonus: now I live in Central America, and swordtails and mollies nibble my toes when I swim in the rivers and waterfalls here! I would love to open a hobby store, but not sure if the government here allows it.