Parrot fish are one of those species I put on the list of "special feeders". Because of their body construction they have a more difficult time in getting at and consuming their food. (I am not a fan of the person who interbred the first pair of fish to develop the parrots, and even less of a fan of the first person to have bought them and encouraged their existence in the hobby)
Because of their difficulties they typically require special feeding habits, along with increased maintenance habits. For this reason I call them a difficult fish to keep, they are high maintenance and time consuming to own.
The first thing I am going to suggest during your next feeding is to take a watch with you, something that tracks seconds and minutes. From the time the first food hits the water until its completely eaten and gone takes how long? Time it. They should be able to completely consume all of the food within 2 minutes. Once the fish food hits the water it begins to break down. Some foods such as flake food will break down faster, but they all go through the process. Broken down food means waste in the water. If the nitrifying bacteria culture in that system is large/populated enough to handle the added waste, then the evidence shows up in elevated nitrate levels. Nitrifying bacteria cultures will populate to handle the regular amount of waste in a given tank, and die back to what is needed when the waste level goes down. In situations where over feeding is regular practice for a long period of time, and enough surface area exists, the bacteria culture will grow enough to meet the needs.
In a situation where there is not sufficient enough bacteria population to keep up with the waste, such as happens when over feeding first begins... then ammonia levels will spike and the tank will appear to go through a mini cycle for no obvious reason.
The only way to know if you are over feeding is to do the time test, do the water testing, and take a good look at the foods you are offering. Blood worms are messy and break down faster than live black worms. Live black worms can survive in the aquarium for an extended period of time before they die, then fish are able to suck them out as they find them, provided the substrate is not too deep. Live brine shrimp will also swim for a short period of time when used in a freshwater tank, plus it prompts the fish's hunt instincts. Live brine is a great way to get vitamins into a fish without having to dose something to the tank water. The brine are soaked in vitamin water where they consume it, then fed directly to the fish. It gives new meaning to "you are what you eat".
The point about the food is to watch what you're giving them based on nutritional content and rate of breakdown, then alter your feedings according to what your testing tells you. Most healthy parrot cichlids can be trained to come up to take food. If after checking all of the things I listed here already and you're still concerned they are not getting enough food, start working with them to teach them to come up for pellet food. I have done this with my oscars and I do this with my 8+ inch fancy Goldfish
, and I do it with my geophagus cichlids, also. The training will require a lot of time and patience, but it is very doable.
Another method that can also help... once you figure out how much they should be getting at a feeding, split it in half and feed twice/day instead of once. Some people break it down even further. The trick to making that work without polluting the water is to first dish up a full portion, then break it down so only that much goes in over the course of a day. The more often they get it the more likely they are to all get something and the fish that tend to bully for food will also usually calm down at feeding time, making it easier for less dominant fish to feed at the same time.
I hope this all helps. If you need more help please let me know.