It doesn't matter how many, or how few, or how large or small the fish or the tank may be; once it's cycled, that just means that it has enough bacteria to handle that bioload, i.e. to process the ammonia produced by that particular population of fish. If you increase the bioload a little bit...add a fish or two...there's going to be a blip in the ammonia level for a short time, perhaps a few hours, until the bacterial colony increases to catch up to this new ammonia production level.
If your tank had a single fish in it, it was cycled for that much ammonia production. Adding another similar-sized fish doubles the ammonia output, and requires the bacterial population to double as well...but even that only takes a day or so and you likely won't even notice a spike in ammonia because it will be over so quickly.
I can't follow exactly what you did from that post but it sounds like you threw several large fish into a sparsely-populated cycled tank, so you might've increased the bioload by a factor or 4 or 5 or even more? That'll take a bit longer to accommodate, and so you are more aware of the spike. Ideally, you would introduce those fish in stages and minimize feeding for a day or so allow for a smooth transition to the higher bioload.
An interesting manipulation of logic brought you to the conclusion that a water change is not necessary or even beneficial...but no, in a case like this, a couple of big water changes would help dilute the ammonia and give your bacterial colony a chance to ramp up to deal with it before it impacts the fish. Maybe those bottled bacteria mentioned by
RyanScanner
would be useful here also, but I don't have any experience with those so I won't comment.
Your green water is a separate but related issue. It's simply algae, which likely exploded into high gear at least partially due to the higher ammonia. Plants do consume ammonia, so the green water is an unsightly but actually helpful way of reducing the ammonia levels somewhat until the bacteria are able to do it. It also helps lower your high nitrate levels to some extent...but not enough to get you out of those pesky water changes.
Water changes are not rocket science; they're about the most basic and easiest part of the fish-keeping hobby, and are the natural answer to almost all of the basic problems, including this one. Don't "hold off" on them because you think you will make things worse; in virtually every case, the opposite is true.