To me, "happy fish" are swimming about and interacting with each other and coming up to be fed. Unhappy fish are gasping for air, or flashing, or lethargic, or have visible injuries or swelling and are not interested in food. (Assuming hibernation is a normal cold weather state, I am referring to their active times of year).
I believe a living pond has healthier water for fish than fresh city treated tap water. I know you are doing water changes to get rid of ammonia per your readings. But how is that much ammonia building up so quickly in the new water? This is what makes me doubt the reading is accurate., or meaningful.
I trust nature and a living pond to take care of itself more than I trust adding a bunch of chemicals and powders to treated city water.
I do not believe that 4 goldfish in a 600 plus gallon pond is overstocked. I have a dozen goldfish in a smaller pond. I also have frogs, toads, insect larvae including dragonfly nymphs. So for anyone who wants to say my water parameters may be off, they may be, but sensitive wildlife is living and thriving so that is a better test for me than the numbers on test kits.
Something still seems off to me about your measurements. I understand you have tried multiple test kits. But do the numbers actually matter if the fish are not dying, and the plants are living? I love my fish too and feel sad if something happens to any of them. Some have said fish should be dead at those readings. If that is the case, are the readings accurate? You are not describing symptoms of ammonia toxicity in your fish.
Posters have described thinking their fish died and they ignored a pond for a year or more without the pump running or maintaining it, then discovering goldfish were alive in it the whole time. Goldfish can survive in nasty flood control canals/ponds, as well as in small glass bowls with no pump or plants. They are very hardy. Of course we want our sweet fish to have a perfect happy clear water home. But they are able to survive in much worse water conditions.
I would try to slow down on water changes and adding chemicals and let the plants and life in your pond find their own balance. It is not sustainable to keep adding chemicals, powders, and doing major water changes. Your pond needs to reach an equilibrium of it's own with your water and your plants and animal and bacteria life. The frequent water changes keep disrupting your pond from reaching a natural state. I trust the water in a living pond with your filters and pumps and plants, much more than I trust tap water with added chemicals for your fish. 4 fish can only make so much waste in a day that the plants and the existing bacteria are helping process. The chemicals are just more things in the water for the plants and fish to be dealing with, that are potentially more toxic than waste from 4 goldfish.
Again, 4 goldfish of any size is not overstocked in your pond! 3 1/2 feet deep is a good sized pond. Are you sure on your dimensions? I thought I was 2-3 feet deep. But when I measured, I am under 2 feet, closer to 18 inches at my pond's deepest, and all of my fish over wintered fine. What are your total dimensions? Do you have pictures you can post so we see what you have?
I am a beginner on this site. My current pond is only about a year old. I had a pond with a waterfall that was bigger at my old house for 12 years. I had no fish die offs. But........it was relatively ignored and I never tested the water. I added water if it got low, occasionally overflowed it to flush it out with well water if there were too many floating leaves. I drained it and probably overcleaned it every few years and added new pond plants. That was the only time I could count my fish, when I got them out into a plastic bin while I did the deeper cleaning of draining and shoveling and scooping out the muck and spraying all the concrete with a hose. The only filter was around the pump so it wouldn't get clogged. There was a massive water celery that I would have to majorly trim from time to time. The goldfish did seem happy and reproduced over time. But, raccoons there too, so it never got over populated. I rarely fed those fish. They grazed on the plants and insects. It was right outside my back door with a bridge over it to the back yard. I miss it. The owners we bought the house from said some of the fish were from when they had moved in 10 years earlier. I did not have the same level of obsession and sitting and staring at my fish that I have now. That first pond was closer to 1000 gallons and 3 feet deep. So I am not a complete novice to keeping a pond and fish alive.
I have had one goldfish die in my current pond in the year or so I have had it. Just the one fish got slow and puffy. All of the others were their normal selves. So I do not believe it was water parameters that killed the one fish and did not affect any of the others. I believe it was some kind of organ failure in that one fish, and it may have been unhealthy from the store. (My other fish deaths/disappearance were raccoons, with scales and some innards left next to the pond. I have put a fence over my pond to save my precious fish from raccoons. They have more chance of escaping if the raccoon can only get a paw in at a time. I can not keep the darn raccoons out of my yard). I watch this pond closely and spend almost an hour a day sitting and staring at it. It is my meditation/relaxation.
I truly care about my specific fish too. I will take them with me if I move from this house!
The advice "stop testing your water, if plants can grow, the water is fine for goldfish" is a quote I got from a local pond store/water plant store owner. I do feel there is wisdom in his words.
My pond is concrete lined and relatively new from last summer. He told me that when I talked to him about how long to wait to add fish, for the concrete to cure and settle.
This discussion makes me want to check my water parameters out of curiosity. But I only have the less accurate test strips.
You are definitely a great fish mom and are putting a lot of time and caring into your lucky fish and pond. Your fish have survived over a year. You were doing something right before the past few months of testing and trying to reach a balance on the test parameters. I understand your fish have grown. But you have added plants and more filtration too.